Viability theory
From MaRDI portal
Publication:5905497
zbMath0755.93003MaRDI QIDQ5905497
Publication date: 18 September 1992
Published in: Systems \& Control: Foundations \& Applications (Search for Journal in Brave)
differential gamesdifferential inclusionsLyapunov functionstracking problemfunctional differential inclusionspartial differential inclusionsviability constraintsset valued analysisViability theoryviability tubes
Research exposition (monographs, survey articles) pertaining to systems and control theory (93-02) Stochastic systems in control theory (general) (93E03) Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control (49-02)
Related Items
Viable control for uncertain nonlinear dynamical systems described by differential inclusions ⋮ Doubly invariant equilibria of linear discrete-time games ⋮ On open-loop and feedback attainability of a closed set for nonlinear control systems ⋮ Global asymptotic stability of neural networks with discontinuous activations ⋮ Inducing strong convergence of trajectories in dynamical systems associated to monotone inclusions with composite structure ⋮ Partial differential equation for evolution of star-shaped reachability domains of differential inclusions ⋮ Efficient solution of ordinary differential equations with a parametric lexicographic linear program embedded ⋮ Maximin, viability and sustainability ⋮ Extension of the concept of invariance and statistically weakly invariant sets of controllable systems ⋮ Viable control of an epidemiological model ⋮ Computing the viability kernel in large state dimension ⋮ Well-posedness for mutational equations under a general type of dissipativity conditions ⋮ Solutions to hybrid inclusions via set and graphical convergence with stability theory applications ⋮ Robust output feedback model predictive control of constrained linear systems ⋮ Dynamical consequences of optimal host feeding on host-parasitoid population dynamics ⋮ Continuous selection of the solution map for one-sided Lipschitz differential inclusions ⋮ Existence and multiplicity results for systems of first-order differential equations via the method of solution-regions ⋮ Improved relaxations for the parametric solutions of ODEs using differential inequalities ⋮ Interval bounds on the solutions of semi-explicit index-one DAEs. II: Computation ⋮ Monotonicity properties for the viable control of discrete-time systems ⋮ Evolutions of tubes under operability constraints ⋮ Systems with distributions and viability theorem ⋮ On the reachable set of inflated singularly perturbed differential equations ⋮ A Peano theorem for fuzzy differential equations with evolving membership grade ⋮ On converse Lyapunov theorems for fluid network models ⋮ Stochastic viability and dynamic programming ⋮ A topological obstruction in a control problem ⋮ Optimized robust control invariance for linear discrete-time systems: theoretical foundations ⋮ Targeted agreement of multiple Lagrangian systems ⋮ Robust time-optimal control of constrained linear systems ⋮ Invariant solutions of differential games with measures: a discontinuous time reparameterization approach ⋮ Neural network for constrained nonsmooth optimization using Tikhonov regularization ⋮ Fixed point approach for weakly asymptotic stability of fractional differential inclusions involving impulsive effects ⋮ Feedback stabilization methods for the solution of nonlinear programming problems ⋮ The abstract Cauchy problem for dissipative operators with respect to metric-like functionals ⋮ The construction of differential inclusions with prescribed attainable sets ⋮ Feasibility in finite time ⋮ Fixed set iterations for relaxed Lipschitz multimaps. ⋮ Verification of discrete time stochastic hybrid systems: a stochastic reach-avoid decision problem ⋮ Optimal extended optical flow and statistical constraints: a result of convergence ⋮ Simple and cumulative regret for continuous noisy optimization ⋮ Viability analysis of an aircraft flight domain for take-off in a windshear ⋮ A dynamic game of coalition formation under ambiguity ⋮ Optimal control problems on manifolds: A dynamic programming approach ⋮ Building strategies to ensure language coexistence in presence of bilingualism ⋮ Stochastic morphological evolution equations ⋮ Weak pullback attractors of setvalued processes. ⋮ Controller synthesis for robust invariance of polynomial dynamical systems using linear programming ⋮ Exact and possible viability for controlled diffusions. ⋮ Optimal control of heterogeneous systems with endogenous domain of heterogeneity ⋮ Dynamical behaviors for discontinuous and delayed neural networks in the framework of Filippov differential inclusions ⋮ Nonsmooth Lyapunov pairs for infinite-dimensional first-order differential inclusions ⋮ Nonemptiness of viability kernels for infinite-dimensional differential inclusions ⋮ Averaging problem for weakly coupled nonexpansive control systems ⋮ Partial differential inclusions of transport type with state constraints ⋮ Robust viability analysis of a controlled epidemiological model ⋮ Contingent solutions to the center manifold equation ⋮ Viability in hybrid systems ⋮ Robust MPC via min-max differential inequalities ⋮ Stochastic optimal control of ultradiffusion processes with application to dynamic portfolio management ⋮ Invariant dual cones for hybrid systems ⋮ Modelling multi-cellular growth using morphological analysis ⋮ The existence of viable trajectories in state-dependent impulsive systems ⋮ Hypercubes are minimal controlled invariants for discrete-time linear systems with quantized scalar input ⋮ A sufficient condition of viability for fractional differential equations with the Caputo derivative ⋮ Angiogenesis inhibition and tumor-immune interactions with chemotherapy by a control set-valued method ⋮ Optimal extended optical flow subject to a statistical constraint ⋮ Robust transferable sets of linear transferring strategies ⋮ Families of semipermeable curves in differential games with the homicidal chauffeur dynamics ⋮ Controlled invariant feasibility - a general approach to enforcing strong feasibility in MPC applied to move-blocking ⋮ Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions ⋮ Distributed control of cooperative target enclosing based on reachability and invariance analysis ⋮ Stability criteria for a class of differential inclusion systems with discrete and distributed time delays ⋮ Discontinuous control problems for non-convex dynamics and near viability for singularly perturbed control systems ⋮ On connections between stochastic differential inclusions and set-valued stochastic differential equations driven by semimartingales ⋮ Calculating the proximal subdifferential via the quasidifferential ⋮ Existence of local and global solutions of fuzzy delay differential inclusions ⋮ On memo-viability of fractional equations with the Caputo derivative ⋮ Existence of asymptotic values for nonexpansive stochastic control systems ⋮ Multi-criteria dynamic decision under uncertainty: a stochastic viability analysis and an application to sustainable fishery management ⋮ Existence and global asymptotic stability of periodic solutions for Hopfield neural networks with discontinuous activations ⋮ Cournot maps for intercepting evader evolutions by a pursuer ⋮ A remark on abstract multiplier conditions for robustness problems ⋮ Grouping for optimal growth ⋮ Output feedback control for systems with constraints and saturations: scalar control case ⋮ Necessary and sufficient conditions for local invariance for semilinear differential inclusions ⋮ Adaptive dynamics in games played by heterogeneous populations ⋮ A polytopic game ⋮ Limits of nonlinear discrete-time control systems with fast subsystems ⋮ Anti-windup via constrained regulation with observers ⋮ Feedback spreading control laws for semilinear distributed parameter systems ⋮ Computing combinatorial types of trajectories in Pfaffian dynamics ⋮ Existence of equilibria of set-valued maps on bounded epi-Lipschitz domains in Hilbert spaces without invariance conditions ⋮ Tracking control for uncertain nonlinear dynamical systems described by differential inclusions ⋮ Semicontinuous solutions of Hamilton-Jacobi-Bellman equations with degenerate state constraints ⋮ Nonlinear state feedback for \(\ell^ 1\) optimal control ⋮ Properties of the reachable set of control systems ⋮ Stability of solutions to Hamilton-Jacobi equations under state constraints ⋮ Conditional viability for impulse differential games ⋮ Uniqueness of solutions to the Hamilton-Jacobi equation: A system theoretic proof ⋮ Unnamed Item ⋮ Stochastic system controller synthesis for reachability specifications encoded by random sets ⋮ Periodic dynamics of delayed Lotka-Volterra competition systems with discontinuous harvesting policies via differential inclusions ⋮ Unnamed Item ⋮ Correspondence of Trap Spaces in Different Models of Bioregulatory Networks ⋮ Linear programming based optimality conditions and approximate solution of a deterministic infinite horizon discounted optimal control problem in discrete time ⋮ Characterization of the optimal trajectories for the averaged dynamics associated to singularly perturbed control systems ⋮ Necessary and sufficient conditions for the nonincrease of scalar functions along solutions to constrained differential inclusions ⋮ Denotational semantics of hybrid automata ⋮ Open-Loop Solvability Operator in Differential Games with Simple Motions in the Plane ⋮ LP-related representations of Cesàro and Abel limits of optimal value functions ⋮ Can protected areas potentially enlarge viability domains for harvesting management? ⋮ Necessary optimality condition for the minimal time crisis relaxing transverse condition via regularization ⋮ Sufficient conditions for forward invariance and contractivity in hybrid inclusions using barrier functions ⋮ Computation of the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints ⋮ Viability, viscosity, and storage functions in model-predictive control with terminal constraints ⋮ Continuously regulated control systems ⋮ Reduction of lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations ⋮ On Near Optimal Control of Systems with Slow Observables ⋮ Optimization of Mayer functional in problems with discrete and differential inclusions and viability constraints ⋮ Multiagent Systems with Compasses ⋮ Invariance of sets under mutational inclusions on metric spaces ⋮ The interaction of economic agents in Cournot duopoly models under ecological conditions: a comparison of organizational modes ⋮ Weakening state constraints in optimal control problems ⋮ Representation theorem and viability property for multidimensional BSDEs and their applications ⋮ A one-layer recurrent neural network for nonsmooth pseudoconvex optimization with quasiconvex inequality and affine equality constraints ⋮ Dynamical Systems and Hamilton–Jacobi–Bellman Equations on the Wasserstein Space and their L2 Representations ⋮ Control theory approach to continuous-time finite state mean field games ⋮ A qualitative game of interest rate adjustments with a nuisance agent ⋮ Discrete approximations and optimality conditions for controlled free-time sweeping processes ⋮ A comparative analysis of sustainable exploitation of renewable resources for different information structures ⋮ A measurable upper semicontinuous viability theorem for tubes ⋮ Invariant closed sets with respect to differential inclusions with time-dependent maximal monotone operators ⋮ Absorption paths and equilibria in quitting games ⋮ On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients ⋮ State-constrained porous media control systems with application to stabilization ⋮ About the minimal time crisis problem ⋮ Hybrid Systems with Memory: Existence and Well-posedness of Generalized Solutions ⋮ Viability Kernels and Capture Basins for Analyzing the Dynamic Behavior: Lorenz Attractors, Julia Sets, and Hutchinson’s Maps ⋮ Linear cone-invariant control systems and their equivalence ⋮ Anticipating Shocks in the State Space: Characterizing Robustness and Building Increasingly Robust Evolutions ⋮ Unnamed Item ⋮ Domain invariance for local solutions of semilinear evolution equations in Hilbert spaces ⋮ Unnamed Item ⋮ Differential Games ⋮ Set invariance under output feedback: a set-dynamics approach ⋮ Unnamed Item ⋮ Guaranteed Characterization of Capture Basins of Nonlinear State-Space Systems ⋮ Unnamed Item ⋮ Differential equations with fuzzy parameters via differential inclusions ⋮ Lyapunov stability using minimum distance control ⋮ Set Theoretic Methods in Model Predictive Control ⋮ Second-order analysis for the time crisis problem ⋮ Asymptotic stability for tracking control of nonlinear uncertain dynamical systems described by differential inclusions. ⋮ Unnamed Item ⋮ Viability Kernels and Control Sets ⋮ Lyapunov functions for second-order differential inclusions: A viability approach ⋮ Human centered processes and decision support systems ⋮ Analyse régionale des systèmes distribués ⋮ A Robust Saturated Strategy for $n$-Player Prisoner's Dilemma ⋮ Global exponential stabilizability for a class of differential inclusion systems with multiple time delays ⋮ Homicidal Chauffeur Game: History and Modern Studies ⋮ Generalized Lyapunov and invariant set theorems for nonlinear dynamical systems ⋮ On the Generalized Duality Principle for State-Constrained Control and State Estimation Under Impulsive Inputs ⋮ Singularly perturbed differential inclusions: An averaging approach ⋮ On nonlocal Cauchy problems for constrained differential inclusions in Euclidean space ⋮ Border Avoidance: Necessary Regularity for Coefficients and Viscosity Approach ⋮ Some algorithms for differential games with two players and one target ⋮ Analysis of Tumor/Effector Cell Dynamics and Decision Support in Therapy ⋮ Real states of stable sliding mode control systems ⋮ Unnamed Item ⋮ Projected Dynamical Systems on Irregular, Non-Euclidean Domains for Nonlinear Optimization ⋮ A tree structure algorithm for optimal control problems with state constraints ⋮ Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability ⋮ Nonconvex Duality and Semicontinuous Proximal Solutions of HJB Equation in Optimal Control ⋮ The Minimum Time Function for the Controlled Moreau's Sweeping Process ⋮ Stability of democracies: a complex systems perspective ⋮ LP Formulations of Discrete Time Long-Run Average Optimal Control Problems: The NonErgodic Case ⋮ SVM Approximation of Value Function Contours in Target Hitting Problems ⋮ Continuity and computability of reachable sets ⋮ On singular perturbations for differential inclusions on the infinite interval ⋮ C.A.s.S.a.n.D.r.A: Computerized Analysis for Supply ChAiN DistRibution Activity ⋮ Population viability in three trophic-level food chains ⋮ On the Computation of Set-Induced Control Lyapunov Functions for Continuous-Time Systems ⋮ Value functions for Bolza problems with discontinuous Lagrangians and Hamilton-Jacobi inequalities ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Invariance of stochastic control systems with deterministic arguments ⋮ Properties of recoverable region and semi-global stabilization in recoverable region for linear systems subject to constraints ⋮ Anti-Lyapunov method for systems of discrete equations ⋮ Strict equilibria of multi-valued maps and common fixed points ⋮ On reachability and minimum cost optimal control ⋮ Boundary value problems for semi-continuous delayed differential inclusions on Riemannian manifolds ⋮ Mutational equations for shapes and vision-based control ⋮ Global dissipativity of non-autonomous BAM neural networks with mixed time-varying delays and discontinuous activations ⋮ Lax-Hopf formula and Max-Plus properties of solutions to Hamilton-Jacobi equations ⋮ A constructive theory of shape ⋮ Linear programming formulations of deterministic infinite horizon optimal control problems in discrete time ⋮ Mathematical modeling of an urban pigeon population subject to local management strategies ⋮ Invariant sets and Lyapunov pairs for differential inclusions with maximal monotone operators ⋮ A viability theorem for set-valued states in a Hilbert space ⋮ Motion planning algorithms for the Dubins Travelling Salesperson Problem ⋮ Immersion and invariance stabilization for a class of nonlinear switched systems with average dwell time ⋮ Optimal control for the evolution of deterministic multi-agent systems ⋮ On nonlinear inclusions in non-smooth domains ⋮ A neurodynamic approach to nonsmooth constrained pseudoconvex optimization problem ⋮ Computation of polytopic invariants for polynomial dynamical systems using linear programming ⋮ Linear programming formulation of long-run average optimal control problem ⋮ Viability in a non-local population model structured by size and spatial position ⋮ A set-valued approach to control immunotherapy ⋮ Discontinuous solutions of Hamilton-Jacobi-Bellman equation under state constraints ⋮ Net Laplacian controllability for joins of signed graphs ⋮ New conditions on synchronization of networks of linearly coupled dynamical systems with non-Lipschitz right-hand sides ⋮ A necessary condition of viability for fractional differential equations with initialization ⋮ Hölder metric regularity of set-valued maps ⋮ Viable states for monotone harvest models ⋮ Uniqueness of the viscosity solution of a constrained Hamilton-Jacobi equation ⋮ Comparing the sustainability of different action policy possibilities: application to the issue of both household survival and forest preservation in the corridor of Fianarantsoa ⋮ Dynamic decentralization of harvesting constraints in the management of tychastic evolution of renewable resources ⋮ Feedback and invariance under uncertainty via set-iterates ⋮ Viability for nonlinear multi-valued reaction-diffusion systems ⋮ Viable solutions of lower semicontinuous quantum stochastic differential inclusions ⋮ On the optimal control of rate-independent soft crawlers ⋮ Feedback spreading controls for semilinar parabolic systems ⋮ Qualitative properties of trajectories of control systems: a survey ⋮ Controllability of differential inclusions ⋮ Hamilton-Jacobi-Bellman equation under states constraints ⋮ On smoothness of solutions to projected differential equations ⋮ Control and optimization in a collision avoidance problem in oscillating systems ⋮ Population growth and Nash equilibria under viability constraints in the commons ⋮ Approximate bisimulation relations for constrained linear systems ⋮ On the existence of a Lipschitz feedback control in a control problem with state constraints ⋮ Olech's correction to the proof of his theorem on existence of solutions to differential inclusions ⋮ Shape evolutions under state constraints: A viability theorem ⋮ Sustainable thresholds for cooperative epidemiological models ⋮ Viability analysis for the sustainable management of renewable resources ⋮ Mutational analysis with transitions whose domains vary in state and that are not necessarily Lipschitz continuous in time ⋮ Viable set computation for hybrid systems ⋮ Viable immersion and invariance control for a class of nonlinear systems and its application to aero-engines ⋮ Invariant sets computation for convex difference inclusions systems ⋮ Strong invariance and one-sided Lipschitz multifunctions ⋮ Stratified semiconcave control-Lyapunov functions and the stabilization problem ⋮ Applications of Ky Fan's inequality on \(\sigma\)-compact set to variational inclusion and \(n\)-person game theory ⋮ Multiallelic polymorphism maintained under unpredictable migration and selection ⋮ Averaging of perturbed one sided Lipschitz differential inclusions ⋮ Lyapunov theorems for systems described by retarded functional differential equations ⋮ On average control generating families for singularly perturbed optimal control problems with long run average optimality criteria ⋮ Stable games and their dynamics ⋮ An anti-diffusive scheme for viability problems ⋮ Pareto fronts of the set of sustainable thresholds for constrained control systems ⋮ Viability of an open set for stochastic control systems ⋮ A novel neural network to nonlinear complex-variable constrained nonconvex optimization ⋮ Discussion on: ``Global regulation of input-saturated discrete-time linear systems subject to persistent disturbances ⋮ Control design for autonomous vehicles: a dynamic optimization perspective ⋮ Robust predictive regulation with invariance constraint ⋮ On stochastic linear systems with zonotopic support sets ⋮ Admissible sets for slowly-varying discrete-time systems ⋮ Preface: DGAA special issue on pursuit-evasion games and differential games with incomplete information ⋮ Generation of dangerous disturbances for flight systems ⋮ Computation of solvability set for differential games in the plane with simple motion and non-convex terminal set ⋮ Collective circular motion of multi-vehicle systems ⋮ Nonsmooth feedback control for multi-agent dynamics ⋮ On associative motor learning by the cerebellar cortex: From Purkinje unit to network with variational learning rules ⋮ Optimization of fully controlled sweeping processes ⋮ Functional differential inclusions and dynamic behaviors for memristor-based BAM neural networks with time-varying delays ⋮ Characterizing sustainability in discrete time ⋮ Existence and Lyapunov pairs for the perturbed sweeping process governed by a fixed set ⋮ Viability discrimination of a class of control systems on a nonsmooth region ⋮ Lyapunov stability of differential inclusions involving prox-regular sets via maximal monotone operators ⋮ Invariance and strict invariance for nonlinear evolution problems with applications ⋮ Viability and invariance of systems on metric spaces ⋮ Viability constraints for computing solutions to the Lighthill-Whitham-Richards model involving partial autonomous vehicle flow ⋮ Computation of robust capture zones using interval-based viability techniques in presence of state uncertainties ⋮ Extended model of impaired cerebral autoregulation in preterm infants: heuristic feedback control ⋮ Modeling and mitigating link-flooding distributed denial-of-service attacks via learning in Stackelberg games ⋮ Existence of solutions for implicit fuzzy differential inclusions ⋮ Determining the viability for hybrid control systems on a region with piecewise smooth boundary ⋮ Towards a quantitative science of sustainability ⋮ Satisficing versus optimality: criteria for sustainability ⋮ Impulse capture basins of sets under impulse control systems ⋮ Averaging and linear programming in some singularly perturbed problems of optimal control ⋮ Viability of fractional differential inclusions ⋮ Backward reachability approach to state-constrained stochastic optimal control problem for jump-diffusion models ⋮ On existence of solutions to differential equations or inclusions remaining in a prescribed closed subset of a finite-dimensional space. ⋮ Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs ⋮ External ellipsoidal approximations for set evolution equations ⋮ Lagrangian methods for approximating the viability kernel in high-dimensional systems
This page was built for publication: Viability theory
