Saturated control of linear systems
As the title suggests the book is focused on the investigation of systems under the action of saturated feedback controls. The control constraints are ensured, for example, by the rescaling/truncation of the magnitudes obtained by an unconstrained feedback control (e.g., see Sections~1.2 and~1.7) Several works in the literature address the case where the control is given in the form of linear state feedback, that is, a linear function of the state. An example is the classical Riccati based feedback associated with classical linear quadratic optimal control problems, where the energy of the controlled system is minimized, and where the control inputs can take arbitrary large values (magnitudes). In real world applications, we cannot expect that such arbitrary magnitudes can be provided by the actuators. For example, the heat provided by a radiator and the acceleration provided by an engine are bounded. Having this in mind, in practice we cannot realize the control given by a linear state feedback if the state is large, but we can still realize the control obtained by rescaling or truncating such control so that the constraints on the bounds for the magnitudes are satisfied. This gives us an idea of saturated feedback controls. The book addresses both discrete-time and continuous-time finite-dimensional systems. The possible presence of uncertainties is a point we should take into account in applications. Indeed, a given system is a mathematical model for a real world process, giving us an approximation of the dynamics of such process. Thus, the difference from the model to the (not fully known) real process can be seen as a model uncertainty or disturbance. Such uncertainties/disturbances are also addressed in the book, for example, see Sections~2.2 and~3.3. In applications we may be not able to measure the entire state of the system. But we may be able to measure part (some components) of the state through suitable sensors. The output of the measurements obtained by the sensors can (if rich enough) be used to construct an estimate of the entire state, for example, through a dynamic Luenberger observer. Such state estimate can then be used to compute an approximation of a state feedback control. The observer design and saturated observer/output-based feedback controls are addressed in Chapter~5. Though the usual control constraints on the magnitude of the controls are the main focus of the book, constraints are also considered on the magnitude of the time derivative of the control (respectively, on the increment of the control, for discrete time systems); see Section~3.2. The stabilization problem (e.g., around an unstable equilibrium) is of particular interest for applications. This problem is addressed in Chapters~7 and~8. The cases of singular and time-delay systems are also addressed in the book, namely, in Chapters~4 and~9, respectively. The book also contains several figures showing the results of numerical simulations. In conclusion, the book addresses several points which are important concerning the control of real world processes which can be modeled by finite-dimensional systems. Thus, it is an interesting reference for engineers and researchers working on the practical implementation of constrained controls.
scientific article; zbMATH DE number 6833094