Control theory from the geometric viewpoint.

zbMath1062.93001MaRDI QIDQ1883272

Yuri L. Sachkov, Andrei A. Agrachev

Publication date: 4 October 2004

Published in: Encyclopaedia of Mathematical Sciences (Search for Journal in Brave)

zbMATH Keywords

optimal controlmaximum principlecurvaturetime-optimal controlrigid bodyfeedback linearizationlinearizabilityFrobenius theoremmoving framesecond-order conditionsattainable setschronological calculuschronological exponentialdifferential-geometric methods in controlL-Q problemrolling bodies

Mathematics Subject Classification ID

Controllability (93B05) Research exposition (monographs, survey articles) pertaining to systems and control theory (93-02) Transformations (93B17) Hamilton-Jacobi equations in mechanics (70H20) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Attainable sets, reachability (93B03) Nonholonomic systems related to the dynamics of a system of particles (70F25) Optimality conditions for problems involving ordinary differential equations (49K15) Motion of a rigid body in contact with a solid surface (70E18) Vector distributions (subbundles of the tangent bundles) (58A30)

Related Items

Barbashin and Krasovskii's asymptotic stability theorem in application to control systems on smooth manifolds, On an optimal flow in a class of nilpotent convex problems, On extensions of sub-Riemannian structures on Lie groups, Conformal equivalence of 3D contact structures on Lie groups, Small-time reachable sets of linear systems with integral control constraints: birth of the shape of a reachable set, Non-degenerate necessary optimality conditions for the optimal control problem with equality-type state constraints, Semi-conical eigenvalue intersections and the ensemble controllability problem for quantum systems, On the Hadamard-Hamel problem and the dynamics of wheeled vehicles, Metamorphosis of images in reproducing kernel Hilbert spaces, A Riemannian approach to Randers geodesics, On the sub-Riemannian geodesic flow for the Goursat distribution, Invariant submanifolds for systems of vector fields of constant rank, Sub-Lagrangians and sub-Hamiltonians on affine bundles, Horizontal holonomy for affine manifolds, On sub-Riemannian and Riemannian structures on the Heisenberg groups, Planar tilting maneuver of a spacecraft: singular arcs in the minimum time problem and chattering, Franks' lemma for \(C^2\)-Mañé perturbations of Riemannian metrics and applications to persistence, A contact covariant approach to optimal control with applications to sub-Riemannian geometry, Maxwell strata and conjugate points in the sub-Riemannian problem on the Lie group SH(2), On sub-Riemannian geodesics in \(\mathrm{SE}(3)\) whose spatial projections do not have cusps, Harnack inequality for hypoelliptic second order partial differential operators, Cut locus of a left invariant Riemannian metric on \(\mathrm{SO}_3\) in the axisymmetric case, Sard property for the endpoint map on some Carnot groups, Second order analysis of control-affine problems with scalar state constraint, Rolling against a sphere: the non-transitive case, Optimal treatment profile during an influenza epidemic, Complex geometry of polygonal linkages, Extremal curves in nilpotent Lie groups, Optimal saturated feedback laws for LQR problems with bounded controls, Clebsch variational principles in field theories and singular solutions of covariant EPDiff equations, Multilayer minimum projection method for nonsmooth strict control Lyapunov function design, Local controllability of 1D linear and nonlinear Schrödinger equations with bilinear control, Designing rendezvous missions with mini-moons using geometric optimal control, A coarea formula for smooth contact mappings of Carnot-Carathéodory spaces, Remarks on global sub-Lorentzian geometry, BRST analysis of general mechanical systems, Asymptotic approach on conjugate points for minimal time bang-bang controls, Conic distributions and accessible sets, Optimal control of Cauchy problem for first-order discrete and partial differential inclusions, Geometric structure-preserving optimal control of a rigid body, On Zermelo-like problems: Gauss-Bonnet inequality and E. Hopf theorem, Dynamics control by a time-varying feedback, Minimum \(L^\infty\) accelerations in Riemannian manifolds, Euler's fluid equations: Optimal control vs optimization, Structural stability investigation of bang-singular-bang optimal controls, Bang-singular-bang extremals: sufficient optimality conditions, Local controllability and non-controllability for a 1D wave equation with bilinear control, Normal forms and reachable sets for analytic Martinet sub-Lorentzian structures of Hamiltonian type, Existence of planar curves minimizing length and curvature, Families of vector fields which generate the group of diffeomorphisms, Microlocal normal forms for regular fully nonlinear two-dimensional control systems, A remark on the potentials of optimal transport maps, Sub-Riemannian structures on 3D Lie groups, Locomotion and control of a self-propelled shape-changing body in a fluid, On the curvature of two-dimensional optimal control systems and Zermelo's navigation problem, On the minimizing properties of the 8-shaped solution of the 3-body problem, Constrained diffeomorphic shape evolution, Optimization of Cauchy problem for partial differential inclusions of parabolic type, Control systems on three-dimensional Lie groups: equivalence and controllability, Extremal trajectories and Maxwell strata in sub-Riemannian problem on group of motions of pseudo-Euclidean plane, Min-max and min-min Stackelberg strategies with closed-loop information structure, The turnpike property in finite-dimensional nonlinear optimal control, Metrics with equatorial singularities on the sphere, Fine properties of basis vector fields on Carnot-Carathéodory spaces under minimal assumptions on smoothness, Geometric control theory and linear switched systems, Fine properties of basis vector fields on Carnot-Carathéodory spaces under minimal smoothness assumptions, Optimal control of epidemics with limited resources, On the Hausdorff volume in sub-Riemannian geometry, A note on hyperbolic flows in sub-Riemannian structures with transverse symmetries, The normal sub-Riemannian geodesic flow on E(2) generated by a left-invariant metric and a right-invariant distribution, A review of geometric optimal control for quantum systems in nuclear magnetic resonance, Optimization of boundary value problems for certain higher-order differential inclusions, The ball-box theorem for a class of corank 1 non-differentiable tangent subbundles, Gauge symmetries in 2D field theory, On certain hyperelliptic signals that are natural controls for nonholonomic motion planning, Rolling manifolds of different dimensions, Pointwise second-order necessary conditions for optimal control problems evolved on Riemannian manifolds, Locally convex topologies and control theory, Controlled motion of a rigid body with internal mechanisms in an ideal incompressible fluid, Quadratic Hamilton-Poisson systems in three dimensions: equivalence, stability, and integration, Minimal time synthesis for a kinematic drone model, Equivalence of variational problems of higher order, Hopf fibration: Geodesics and distances, Rate limited time optimal control of a planar pendulum, Sub-Riemannian geodesics on the three-dimensional solvable non-nilpotent Lie group \(\mathrm{SOLV}^-\), Optimal control of elliptic differential inclusions with Dirichlet and Neumann boundary conditions, High-order sufficient conditions for configuration tracking of affine connection control systems, A simple proof of the Pontryagin maximum principle on manifolds, Sub-Lorentzian structures in \(\mathbb {R}^4\): left-invariance and conformal normal forms, Symmetric Riemannian problem on the group of proper isometries of hyperbolic plane, An efficient cost reduction procedure for bounded-control LQR problems, On the lack of semiconcavity of the subRiemannian distance in a class of Carnot groups, On conjugate times of LQ optimal control problems, On the essential self-adjointness of singular sub-Laplacians, Shortest and straightest geodesics in sub-Riemannian geometry, Strong local optimality for a bang-bang-singular extremal: general constraints, Sub-Riemannian geometry on infinite-dimensional manifolds, Linearisation of tautological control systems, Local properties of almost-Riemannian structures in dimension 3, Optimal control of differential inclusions on manifolds, Quantum confinement on non-complete Riemannian manifolds, Solution to the HJB equation for LQR-type problems on compact connected Lie groups, On the analysis of nonlinear nilpotent switched systems using the Hall-Sussmann system, Geodesics and curvatures of special sub-Riemannian metrics on Lie groups, Cut locus in the sub-Riemannian problem on Engel group, Global problems for differential inclusions. Kalman and Vyshnegradskii problems and Chua circuits, Navier-Stokes equation on the rectangle: Controllability by means of low mode forcing, Construction and comparison of multidimensional spectral variational integrators and spectral collocation methods, Stability analysis of switched systems using variational principles: An introduction, Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy, Why are normal sub-Riemannian extremals locally minimizing?, Approximate controllability of three-dimensional Navier-Stokes equations, Third-order nilpotency, nice reachability and asymptotic stability, A support and density theorem for Markovian rough paths, Non-integrability of the minimum-time Kepler problem, A drift-free left invariant control system on the Lie group \(\mathrm{SO}(3) \times \mathbb R^3 \times \mathbb R^3\), Diameter of the Berger sphere, Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators, Nilpotent \((n, n(n + 1)/2)\) sub-Riemannian problem, An algorithm for optimization of cereal output, Explicit solutions of the \({\mathfrak{a}_1}\)-type Lie-Scheffers system and a general Riccati equation, Hamiltonian coupling of electromagnetic field and matter, Dynamic programming principle of control systems on manifolds and its relations to maximum principle, Presymplectic high order maximum principle, Optimal control of the motion of a helical body in a liquid using rotors, An intrinsic formulation of the problem on rolling manifolds, Almost exponential maps and integrability results for a class of horizontally regular vector fields, Lipschitz classification of almost-Riemannian distances on compact oriented surfaces, \(\Gamma \)-convergence of variational functionals with boundary terms in Stein manifolds, Contact geometry of the Pontryagin maximum principle, Observers for invariant systems on Lie groups with biased input measurements and homogeneous outputs, Rolling of manifolds without spinning, Optimal control and applications to aerospace: some results and challenges, Controllability and time optimal control for low Reynolds numbers swimmers, Symmetries of the rolling model, Markov-Dubins path via optimal control theory, Rolling manifolds on space forms, Tracking of lines in spherical images via sub-Riemannian geodesics in \(\mathrm{SO}(3)\), Optimal sampled-data control, and generalizations on time scales, On symmetries in time optimal control, sub-Riemannian geometries, and the \(K-P\) problem, Free time optimization of second-order differential inclusions with endpoint constraints, Constraint control of nonholonomic mechanical systems, Geometric optimal control and applications to aerospace, Second-order recursive filtering on the rigid-motion Lie group \(\mathrm{SE}_3\) based on nonlinear observations, Second order necessary and sufficient optimality conditions for singular solutions of partially-affine control problems, A discrete-time Pontryagin maximum principle on matrix Lie groups, Time-optimal trajectories of generic control-affine systems have at worst iterated Fuller singularities, Heuristic determination of resolving controls for exact and approximate controllability of nonlinear dynamic systems, A Bonnet-Myers type theorem for quaternionic contact structures, Optimal transport over nonlinear systems via infinitesimal generators on graphs, Gaussian estimates for hypoelliptic operators via optimal control, Strong local optimality for generalized L1 optimal control problems, A geometric approach for the optimal control of difference inclusions, Optimal bacterial resource allocation: metabolite production in continuous bioreactors, Sub-Finsler geodesics on the Cartan group, Besicovitch covering property on graded groups and applications to measure differentiation, Quadratic Hamilton-Poisson systems on \(\mathfrak{se}(1,1)^{*}_{-}\): the inhomogeneous case, On a certain sub-Riemannian geodesic flow on the Heisenberg group, Control sets of linear systems on semi-simple Lie groups, Optimal strokes for low Reynolds number swimmers: an example, On the Whitney extension property for continuously differentiable horizontal curves in sub-Riemannian manifolds, Optimality of Euler's elasticae, A simplification of the Agrachev-Gamkrelidze second-order variation for bang-bang controls, Integrability of continuous bundles, Value function for regional control problems via dynamic programming and Pontryagin maximum principle, The geodesics of a sub-Riemannian metric on the group of semiaffine transformations of the Euclidean plane, Any sub-Riemannian metric has points of smoothness, Local geometry of nonregular weighted quasimetric Carnot-Carathéodory spaces, Two-dimensional almost-Riemannian structures with tangency points, On the algebraic characterization of invariant sets of switched linear systems, Local regularity of optimal trajectories for control problems with general boundary conditions, Control problems with differential constraints of higher order, Mass transportation on sub-Riemannian manifolds, Revisiting parallel car parking problem, Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups, Sets with constant normal in Carnot groups: properties and examples, Time-extremal navigation in arbitrary winds on conformally flat Riemannian manifolds, A short guide through integration theorems of generalized distributions, Multiple solutions in Euler's elastic problem, Maxwell strata and cut locus in the sub-Riemannian problem on the Engel group, Extremal controls in the sub-Riemannian problem on the group of motions of Euclidean space, An abnormal set for the \((2,3,5,8)\)-distribution, Controllability of the discrete-spectrum Schrödinger equation driven by an external field, Line-of-sight guidance control using video images, Symmetries and properties of the energy-Casimir mapping in the ball-plate problem, Optimal paths for variants of the 2D and 3D Reeds-Shepp car with applications in image analysis, On the stabilization problem for nonholonomic distributions, Singular arcs in the generalized Goddard's problem, The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups, Properties of reachable sets in the sub-Lorentzian geometry, Nonlinear subelliptic equations, Dissipativity theory for discontinuous dynamical systems: basic input, state, and output properties, and finite-time stability of feedback interconnections, Geometric approach to Pontryagin's maximum principle, Control theory on Lie groups, Generalized solutions for singular optimal control problems, On curvature and feedback classification of two-dimensional optimal control systems, Solution to Euler's elastic problem, Transformations of control systems for the investigation of pulse modes, Approximate solution of two-point boundary value problems for linear in control systems, Controllability on the group of diffeomorphisms, Neighboring extremal optimal control for mechanical systems on Riemannian manifolds, The general solution for affine control systems on Lie groups, A simple construction of recursion operators for multidimensional dispersionless integrable systems, The polynomial sub-Riemannian differentiability of some Hölder mappings of Carnot groups, Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups, Controlling of a mobile robot with a trailer and its nilpotent approximation, Relation between Euler's elasticae and sub-Riemannian geodesics on \(\mathrm{SE}(2)\), Control of the motion of a helical body in a fluid using rotors, \(\mathrm{L}^1\)-optimality conditions for the circular restricted three-body problem, Small time asymptotics on the diagonal for Hörmander's type hypoelliptic operators, Cut locus and optimal synthesis in sub-Riemannian problem on the Lie group SH(2), Control of body motion in an ideal fluid using the internal mass and the rotor in the presence of circulation around the body, Pure rolling motion of hyperquadrics in pseudo-Euclidean spaces, Varieties of minimal rational tangents of unbendable rational curves subordinate to contact structures, Optimization of switchable systems' trajectories, Minimum fuel control of the planar circular restricted three-body problem, Rolling balls and octonions, Introducing sub-Riemannian and sub-Finsler billiards, Time optimal control for a mobile robot with a communication objective, Turnpike property in optimal microbial metabolite production, Geometric conditions for the existence of a rolling without twisting or slipping, Sub-Riemannian geodesics and heat operator on odd dimensional spheres, Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups with three-dimensional generating distributions, On Liouville-type theorems and the uniqueness of the positive Cauchy problem for a class of hypoelliptic operators, Sub-Riemannian geodesics in \(\mathrm{SO}(3)\) with application to vessel tracking in spherical images of retina, Control systems on nilpotent Lie groups of dimension \(\leq 4\): equivalence and classification, Deformation of piecewise differentiable curves in constrained variational calculus, Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions, Switching in time-optimal problem: the 3D case with 2D control, A simple proof of the discrete time geometric Pontryagin maximum principle on smooth manifolds, Homotopically invisible singular curves, Periodic controls in step 2 strictly convex sub-Finsler problems, Linear-quadratic optimal sampled-data control problems: convergence result and Riccati theory, Sub-Riemannian geometry and finite time thermodynamics. I: The stochastic oscillator, Bakry-Émery curvature and model spaces in sub-Riemannian geometry, A dynamical approach to the Sard problem in Carnot groups, Sufficient optimality conditions for hybrid systems of variable dimension, Sub-Riemannian geometry and geodesics in Banach manifolds, A local solution to the Navier-Stokes equations on manifolds via stochastic representation, Horizontal holonomy and foliated manifolds, Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics, Higher dimensional holonomy map for rules submanifolds in graded manifolds, Geometrical optical illusion via sub-Riemannian geodesics in the roto-translation group, The geometry of differential constraints for a class of evolution PDEs, Jacobi fields in optimal control: one-dimensional variations, On duality in second-order discrete and differential inclusions with delay, On geometry of vector fields, Maximal determinants of Schrödinger operators on bounded intervals, An abstract cell model that describes the self-organization of cell function in living systems, Second order necessary conditions for endpoints-constrained optimal control problems on Riemannian manifolds, Branching geodesics in sub-Riemannian geometry, Conjugate points in the generalized Dido problem, Coadjoint orbits and time-optimal problems for step-2 free nilpotent Lie groups, Control of locomotion systems and dynamics in relative periodic orbits, Generalized loxodromes with application to time-optimal navigation in arbitrary wind, On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies, Robustness under control sampling of reachability in fixed time for nonlinear control systems, Jacobi fields in optimal control: Morse and Maslov indices, Casimir functions of free nilpotent Lie groups of steps 3 and 4, Explicit formulae for geodesics in left-invariant sub-Finsler problems on Heisenberg groups via convex trigonometry, Control homotopy of trajectories, Conjugate time in the sub-Riemannian problem on the Cartan group, Controllability results for the rolling of 2-dimensional against 3-dimensional Riemannian manifolds. I, Periodic time-optimal controls on two-step free-nilpotent Lie groups, Coadjoint orbits of three-step free nilpotent Lie groups and time-optimal control problem, Explicit solutions for a series of optimization problems with 2-dimensional control via convex trigonometry, On switching properties of time optimal controls for linear ODEs, Local contact sub-Finslerian geometry for maximum norms in dimension 3, Association fields via cuspless sub-Riemannian geodesics in SE(2), Extension of chronological calculus for dynamical systems on manifolds, Cost-extended control systems on Lie groups, Controllability on infinite-dimensional manifolds: a Chow-Rashevsky theorem, Exponential mapping in Euler's elastic problem, A second-order maximum principle for discrete-time bilinear control systems with applications to discrete-time linear switched systems, Destruction of dissipative structures under random actions, Heat kernel asymptotics on sub-Riemannian manifolds with symmetries and applications to the bi-Heisenberg group, Legendre's necessary condition for fractional Bolza functionals with mixed initial/final constraints, Deep learning as optimal control problems: models and numerical methods, A unifying approach for rolling symmetric spaces, Approximately controllable finite-dimensional bilinear systems are controllable, Effective adiabatic control of a decoupled Hamiltonian obtained by rotating wave approximation, Sub-Finsler structures on the Engel group, Stochastic completeness and gradient representations for Sub-Riemannian manifolds, Spectrum of the second variation, A sub-Finsler problem on the Cartan group, Neighborhood of the second-order singular regime in problems with control in a disk, Optimal horizontal joinability on the Engel group, Dual formulation of the lemma on substitution homomorphisms, Optimal control of epidemic size and duration with limited resources, Optimal strokes for the 4-sphere swimmer at low Reynolds number in the regime of small deformations, H-type foliations, Aspects of control theory on infinite-dimensional Lie groups and \(G\)-manifolds, Shape deformation analysis from the optimal control viewpoint, Quasi-shuffle algebras in non-commutative stochastic calculus, BV functions and sets of finite perimeter in sub-Riemannian manifolds, Optimization of neutral functional-differential inclusions, Lyapunov and minimum-time path planning for drones, Variational formulas for curves of fixed degree, Classical and quantum controllability of a rotating asymmetric molecule, Extremal controls for the Duits car, On a class of controlled differential variational inequalities, A reverse isoperimetric inequality for planar (α, β)-convex bodies, Structural stability without coercivity, Pontryagin maximum principle, (co)adjoint representation, and normal geodesics of left-invariant (sub-)Finsler metrics on Lie groups, Sub-Riemannian geodesics on SL(2,ℝ), Unnamed Item, Geodesic fields for Pontryagin type C⁰-Finsler manifolds, On Singularities of Minimum Time Control-Affine Systems, Left-invariant optimal control problems on Lie groups: classification and problems integrable by elementary functions, Unbounded Control, Infimum Gaps, and Higher Order Normality, Unnamed Item, Time minimization problem on the group of motions of a plane with admissible control in a half-disc, Application of maximum principle to optimization of production and storage costs, Index theorems for graph-parametrized optimal control problems, Time-optimal control strategies for tungiasis diseases with limited resources, Linear turnpike theorem, Control of multi-agent systems: results, open problems, and applications, The application of a universal separating vector lemma to optimal sampled-data control problems with nonsmooth Mayer cost function, Lipschitz Carnot-Carathéodory structures and their limits, Sub-Lorentzian distance and spheres on the Heisenberg group, The sub-Riemannian geometry of screw motions with constant pitch, On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation, On optimization of coherent and incoherent controls for two-level quantum systems, Front asymptotics of a flat sub-Riemannian structure on the Engel distribution, Lie algebras and integrable systems: elastic curves and rolling geodesics, High-order splines on Riemannian manifolds, Extremal trajectories in a time-optimal problem on the group of motions of a plane with admissible control in a circular sector, Abnormal trajectories in the sub-Riemannian \((2,3,5,8)\) problem, Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry, Generic properties of first-order mean field games, Operators arising as second variation of optimal control problems and their spectral asymptotics, Lorentzian geometry on the Lobachevsky plane, Optimal Control of the Controlled Lotka–Volterra Equations with Applications. The Permanent Case, Heat kernels on unit spheres and applications to graph kernels, On the Pontryagin Maximum Principle under differential constraints of higher order, Dynamical optimal transport of nonlinear control-affine systems, Deep learning approximation of diffeomorphisms via linear-control systems, Controlling non-controllable scallops, Optimal control of ensembles of dynamical systems, Solution curve for linear control systems on Lie groups, Second order optimality conditions for optimal control problems on Riemannian manifolds, A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems, Fronts of control-affine systems in R^3, Functional determinants for the second variation, New second-order optimality conditions in sub-riemannian geometry, Control Sets of Linear Control Systems on ℝ². The Complex Case, Local \(L^1\) sub-Finsler geometry in dimension 3: non-generic cases, Prolongations, invariants, and fundamental identities of geometric structures, Fuller Singularities for Generic Control-Affine Systems with an Even Number of Controls, Symmetries in left-invariant optimal control problems, Sub-Riemannian Geometry in Image Processing and Modeling of the Human Visual System, Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems, Symmetries and Parameterization of Abnormal Extremals in the Sub-Riemannian Problem with the Growth Vector (2, 3, 5, 8), Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints, Orbit equivalence of linear systems on manifolds and semigroup actions on homogeneous spaces, Theory of Differential Inclusions and Its Application in Mechanics, Classical and Quantum Controllability of a Rotating Symmetric Molecule, Causality and Control Systems, Asymptotic Controllability and Lyapunov-like Functions Determined by Lie Brackets, The structure of abnormal extremals in a sub-Riemannian problem with growth vector, Controllabilty and stability analysis on a group associated with Black-Scholes equation, Curvature: A Variational Approach, Minimal time trajectories for two-level quantum systems with two bounded controls, The geometric convexity on SE(3) and its application to the formation tracking in multi-vehicle systems, Homotopy properties of horizontal loop spaces and applications to closed sub-Riemannian geodesics, On the Regularity of Nonlinear Subelliptic Equations, Rolling Problems on Spaces of Constant Curvature, Minimum Time Optimality of a Partially Singular Arc: Second Order Conditions, Left-Invariant Sub-Riemannian Engel Structures: Abnormal Geodesics and Integrability, Continuity of optimal control costs and its application to weak KAM theory, Optimization Methods on Riemannian Manifolds via Extremum Seeking Algorithms, Resonance of minimizers forn-level quantum systems with an arbitrary cost, On Small-Time Local Controllability, Infinite Geodesics and Isometric Embeddings in Carnot Groups of Step 2, Homogeneous spaces with inner metric and with integrable invariant distributions, Homogeneous spaces with inner metric and with integrable invariant distributions, A Higher-Order Maximum Principle for Impulsive Optimal Control Problems, Antipodal Points and Diameter of a Sphere, The Discrete-Time Geometric Maximum Principle, Square-Root Metric Regularity and Related Stability Theorems for Smooth Mappings, A formula for Popp's volume in sub-Riemannian geometry, SUB-RIEMANNIAN RICCI CURVATURES AND UNIVERSAL DIAMETER BOUNDS FOR 3-SASAKIAN MANIFOLDS, Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry, A Zermelo navigation problem with a vortex singularity, Normal forms for the endpoint map near nice singular curves for rank-two distributions, Singular extremals inL¹-optimal control problems: sufficient optimality conditions, DUALITY OF (2, 3, 5)-DISTRIBUTIONS AND LAGRANGIAN CONE STRUCTURES, Morse Families In Optimal Control Problems, On the Controllability of the Rolling Problem onto the Hyperbolic $n$-space, Feedback control of charged ideal fluids, Extension of PID Regulators to Dynamical Systems on Smooth Manifolds (M-PID), Unnamed Item, Worst Exponential Decay Rate for Degenerate Gradient Flows Subject to Persistent Excitation, A minimal time optimal control for a drone landing problem, Second-Order Necessary Conditions for Optimal Control Problems with Endpoints-Constraints and Convex Control-Constraints, Dynamical Analysis and Optimization of a Generalized Resource Allocation Model of Microbial Growth, Non-integrability of the optimal control problem for n-level quantum systems, Reachable sets for two-level open quantum systems driven by coherent and incoherent controls, Homogeneous geodesics in sub-Riemannian geometry, A gradient flow equation for optimal control problems with end-point cost, HJ inequalities involving Lie brackets and feedback stabilizability with cost regulation, On the strong local optimality for state-constrained control-affine problems, Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions, ``Good Lie brackets for control affine systems, On Global Approximate Controllability of a Quantum Particle in a Box by Moving Walls, Traveling along horizontal broken geodesics of a homogeneous Finsler submersion, Horizontal joinability on 5-dimensional 2-step Carnot groups with a codimension 2 horizontal distribution, Higher order Goh conditions for singular extremals of corank 1, Unnamed Item, Shape splines and stochastic shape evolutions: A second order point of view, Measure contraction properties of Carnot groups, Low Reynolds number swimming and controllability, Two Applications of Geometric Optimal Control to the Dynamics of Spin Particles, Approximation of a switched linear system by a nonswitched homogeneous polynomial system, Heat content asymptotics for sub-Riemannian manifolds, Particular extremals in the optimal control problems of the reorientation of an asymmetric rotating body, Strong Local Optimality for a Bang-Bang-Singular Extremal: The Fixed-Free Case, Extremal curves on Stiefel and Grassmann manifolds, Stabilization with arbitrary convergence rate for the Schrödinger equation subjected to an input time delay, Semigenerated Carnot algebras and applications to sub-Riemannian perimeter, Liouville integrability of sub-Riemannian problems on Carnot groups of step 4 or greater, Exact Controllability in Projections of the Bilinear Schrödinger Equation, Controllability implies mixing. I. Convergence in the total variation metric, Ensemble qubit controllability with a single control via adiabatic and rotating wave approximations, Optimal spiral-like solutions near a singular extremal in a two-input control problem, Cumulant-cumulant relations in free probability theory from Magnus' expansion, Geometry of orbits of vector fields and singular foliations, Landmarks for Neurogeometry, Cuspless Sub-Riemannian Geodesics within the Euclidean Motion Group SE(d), Control on the manifolds of mappings with a view to the deep learning, Symmetric spaces rolling on flat spaces, Complexity of Control-Affine Motion Planning, On geometry of 2-nondegenerate CR structures of hypersurface type and flag structures on leaf spaces of Levi foliations, On expansions for nonlinear systems error estimates and convergence issues, Optimality of broken extremals, Control systems on the Engel group, Local (sub)-Finslerian geometry for the maximum norms in dimension 2, A weak spectral condition for the controllability of the bilinear Schrödinger equation with application to the control of a rotating planar molecule, Optimal Control Problems with Symmetry Breaking Cost Functions, The structure of the attractor of shapes of reachable sets, Sub-Lorentzian problem on the Heisenberg group, Solving quantum optimal control problems using Clebsch variables and Lin constraints, On the Set of Points of Smoothness for the Value Function of Affine Optimal Control Problems, Fastest planar motion trajectories with unlimited curvature, Almost-Riemannian manifolds do not satisfy the curvature-dimension condition, Sub-Riemannian Cartan sphere, Invariant Control Systems on Lie Groups, Integrability of dominated decompositions on three-dimensional manifolds, On inverse optimal control problems of human locomotion: stability and robustness of the minimizers, Asymptotics of Maxwell time in the plate-ball problem, Conjugate points in nilpotent sub-Riemannian problem on the Engel group, Trace heat kernel asymptotics in 3D contact sub-Riemannian geometry, Displacement interpolations from a Hamiltonian point of view, Generic transitivity for couples of Hamiltonians, Normal forms for sub-Lorentzian metrics supported on Engel type distributions, Multi-input Schrödinger equation: controllability, tracking, and application to the quantum angular momentum, The structure of reachable sets and geometric optimality of singular trajectories for certain affine control systems in \(\mathbb R^{3}\). The sub-Lorentzian approach, Metric geometry of nonregular weighted Carnot-Carathéodory spaces, Extension to infinite dimensions of a stochastic second-order model associated with shape splines, The Hopf-Lax formula in Carnot groups: a control theoretic approach, The Laplace-Beltrami operator in almost-Riemannian geometry, Lie Theory for Quantum Control, Local Controllability for Abnormal Systems, Controllability and second-order necessary conditions for optimality, Minimum-time strong optimality of a singular arc: The multi-input non involutive case, Optimal Attitude Control with Two Rotation Axes, Continuity of Pontryagin Extremals with Respect to Delays in Nonlinear Optimal Control, Time-optimal control of quantum lambda systems in the KP configuration, Spin dynamics: A paradigm for time optimal control on compact Lie groups, Data-Driven Sub-Riemannian Geodesics in SE(2), Sub-Riemannian Methods in Shape Analysis, Rolling Maps and Nonlinear Data, Control in the Spaces of Ensembles of Points, Third order open mapping theorems and applications to the end-point map, Optimality of a time-dependent treatment profile during an epidemic, Optimal Bang-Bang Trajectories in Sub-Finsler Problems on the Engel Group, Maxwell strata in sub-Riemannian problem on the group of motions of a plane, On the geometry of rolling and interpolation curves on \(S^n\), \(\mathrm{SO}_n\), and Grassmann manifolds, Nonholonomic Riemann and Weyl tensors for flag manifolds, Second order optimality conditions in the smooth case and applications in optimal control, Smooth optimal synthesis for infinite horizon variational problems, Lie-algebraic stability conditions for nonlinear switched systems and differential inclusions, On the isoperimetric problem in the Heisenberg group \(\mathbb H^n\), Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane, Unnamed Item, Minimum Time Control of the Rocket Attitude Reorientation Associated with Orbit Dynamics, Submersions, Hamiltonian Systems, and Optimal Solutions to the Rolling Manifolds Problem, A PDE Approach to Data-Driven Sub-Riemannian Geodesics in $SE$(2), Morphological and linear scale spaces for fiber enhancement in DW-MRI, Ricci curvature type lower bounds for sub-Riemannian structures on Sasakian manifolds., Duality on geodesics of Cartan distributions and sub-Riemannian pseudo-product structures, Duality of singular paths for \((2,3,5)\)-distributions, $\mathrm{L^1}$-Minimization for Mechanical Systems, Comparison theorems for conjugate points in sub-Riemannian geometry, Non-minimality of corners in subriemannian geometry, Sufficient Conditions for a Path-Connected Set of Local Solutions to an Optimal Control Problem, Principal Pivot Transforms of Quasidefinite Matrices and Semidefinite Lagrangian Subspaces, The smooth continuation method in optimal control with an application to quantum systems, A Frobenius theorem for corank-1 continuous distributions in dimensions two and three, Speed-Gradient Control of the Brockett Integrator, Optimal transportation under nonholonomic constraints, Minimal surfaces in sub-Riemannian manifolds and structure of their singular sets in the(2,3)case, Almost-Riemannian Geometry on Lie Groups, Ensemble controllability by Lie algebraic methods, An estimation of the controllability time for single-input systems on compact Lie Groups, Unnamed Item, Invariance entropy for topological semigroup actions, Switching in Time-Optimal Problem with Control in a Ball