Georges Bitsoris

Feedback control of linear discrete-time systems under state and control constraints

In this paper the problem of stabilizing linear discrete-time systems under state and control linear constraints is studied. Based on the concept of positive invariance, existence conditions of linear state feedback control laws respecting both the constraints are established. These conditions are then translated into an algorithm of linear programming.

Positively Invariant Polyhedral Sets of Discrete-time Linear Systems

The problem of the existence of positively invariant polyhedral sets for linear discrete-time dynamical systems is studied. In the first part of the paper, necessary and sufficient conditions for a...

On the positive invariance of polyhedral sets for discrete-time systems

Abstract In this note, necessary and sufficient conditions for a polyhedral set to be a positively invariant set of a linear discrete-time system are established.

Constrained regulation of linear continuous-time dynamical systems

Abstract In this paper the Linear Constrained Regulation Problem (LCRP) for continuous-time dynamical systems is studied. The first part of the paper deals with the existence of linear state-feedback control laws that transfer asymptotically to the origin all initial states belonging to a given polyhedral subset of the state space, while respecting linear constraints on both state and control vectors. Then, the LCRP is formulated as an optimization problem which can be solved by applying linear programming techniques.

Constrained regulation of linear systems

Abstract In this paper the Linear Constrained Regulation Problem without an assigned set of initial states is investigated. This problem consists of the determination of a linear state feedback control law and of a set of admissible initial states D , so that every trajectory of the resulting closed-loop system which emanates from the set converges asymptotically to the origin without violation of the control constraints. By applying well-known results on the positive invariance of polyhedral sets, an eigenstructure assignment approach to this problem is established. If the number of unstable open-loop eigenvalues does not exceed the number of control variables, then this approach enables one to derive a linear state-feedback stabilizing control law which makes the set of states where the control constraints are respected positively invariant. This positively invariant set is the maximal admissible set of initial states for the control law under consideration. For the case where the number of control variables is greater than the number of the unstable open-loop eigenvalues, a modified algorithm is proposed.

Comparison principle, positive invariance and constrained regulation of nonlinear systems

Abstract In this paper the comparison principle is applied to the design of feedback controllers for nonlinear discrete-time systems subject to physical constraints. First, the connection between the comparison principle and the existence of positively invariant sets of a special form is established and polyhedral positively invariant sets for nonlinear systems are obtained. Then these results are applied to the determination of state feedback control laws that transfer to the origin all initial states of a prespecified region of the state-space without violation of physical constraints on the control vector.

Optimization approach to the linear constrained regulation problem for discrete-time systems

The linear constrained regulation problem for discrete-time systems is studied and a design algorithm for a linear constrained state-feedback controller is developed. The approach presented is based on the properties of positive invariant polyhedral sets of linear systems. The first part of the paper deals with the problem of the existence of linear state-feedback control laws that transfer asymptotically to the origin all initial stales belonging to a polyhedral subset of the state space while linear constraints on the control vector are satisfied. Then, an optimization approach for the derivation of a solution to the linear constrained regulation problem is established.

Stabilization of Bilinear Power Converters by Affine State Feedback Under Input and State Constraints

This brief presents a novel systematic procedure for the synthesis of affine state-feedback control laws for power converters. The proposed synthesis method is applicable to power converters with a bilinear averaged model and comes with a guarantee of closed-loop stability under hard state and input constraints. The low complexity of the resulting control law translates into a reduced cost of the control hardware, while nonconservative constraint handling yields a higher reliability of the power converter. Moreover, the incorporation of state constraints in controller synthesis can be exploited to achieve a higher power density for the converter. The effectiveness of the proposed controller synthesis method is illustrated on a buck-boost converter case study. Both simulation and real-time experimental results are reported.

Stability analysis of non-linear dynamical systems

This paper examines the possibility of using non-linear comparison systems in the stability analysis of non-linear dynamical systems. Stability criteria and estimates of the stability region of non-linear comparison systems are established. It is shown that the use of non-linear comparison systems may lead to less conservative results than those obtained by linear ones.

On the Polyhedral Set-Invariance Conditions for Time-Delay Systems

Abstract In this paper the concept of set invariance for time-delay systems is introduced with a specific attention to the linear discrete-time case. We are interested in the definition of a D(elay) -invariant set with respect to a bounded polyhedral subset of the state-space. D -invariance conditions are derived based on the Minkowski addition in a first stage, and subsequently translated in feasibility-based tests in order to obtain an efficient computation time