Daniele Corona

Optimal control of continuous-time switched affine systems

This paper deals with optimal control of switched piecewise affine autonomous systems, where the objective is to minimize a performance index over an infinite time horizon. We assume that the switching sequence has a finite length, and that the decision variables are the switching instants and the sequence of operating modes. We present two different approaches for solving such an optimal control problem. The first approach iterates between a procedure that finds an optimal switching sequence of modes, and a procedure that finds the optimal switching instants. The second approach is inspired by dynamic programming and identifies the regions of the state space where an optimal mode switch should occur, therefore providing a state feedback control law.

Marking estimation of Petri nets with silent transitions

In this paper we deal with the problem of estimating the marking of a labeled Petri net system based on the observation of transitions labels. In particular, we assume that a certain number of transitions are labeled with the empty string /spl epsi/, while a different label taken from a given alphabet is assigned to all the other transitions. Transitions labeled with the empty string are called silent because their firing cannot be observed. Under some technical assumptions on the structure of the T/sub /spl epsiv// -induced subnet, where T/sub /spl epsiv// denotes the set of silent transitions, we formally prove that the set of markings consistent with the observed word can be represented by a linear system with a fixed structure that does not depend on the length of the observed word.

State Estimation of λ-free Labeled Petri Nets with Contact-Free Nondeterministic Transitions*

In this paper we deal with the problem of estimating the marking of a labeled Petri net with nondeterministic transitions. In particular, we consider the case in which nondeterminism is due to the presence of transitions that share the same label and that can be simultaneously enabled. Under the assumption that: the structure of the net is known, the initial marking is known, the transition labels can be observed, the nondeterministic transitions are contact-free, we present a technique for characterizing the set of markings that are consistent with the actual observation. More precisely, we show that the set of markings consistent with an observed word can be represented by a linear system with a fixed structure that does not depend on the length of the observed word.

STABILIZATION OF SWITCHED SYSTEMS VIA OPTIMAL CONTROL

Abstract In this paper we consider switched systems composed of LTI non Hurwitz dynamics and we deal with the problem of computing an appropriate switching law such that the controlled system is globally asymptotically stable. We first present a method to design a feedback control law that minimizes a linear quadratic performance index when an infinite number of switches is allowed and at least one dynamics is Hurwitz. Then, we show that this approach can be applied to stabilize switched systems whose modes are all unstable, by simply applying the proposed procedure to a “dummy” system, augmented with a stable dynamics. If the system with unstable modes is globally exponentially stabilizable, then our method is guaranteed to provide the feedback control law that minimizes the chosen quadratic performance index, and that guarantees the closed loop system to be globally asymptotically stable.

Optimal State-Feedback Quadratic Regulation of Linear Hybrid Automata

Abstract For linear hybrid automata, namely switched linear autonomous systems whose mode of operation is determined by a controlled automaton, in this paper we face the problem of optimal control, where the objective is to minimize a quadratic performance index over an infinite time horizon. The quantities to be optimized are the sequence of switching times and the sequence of modes (or “locations”), under the following constraints: the sequence of modes has a finite length; the discrete dynamics of the automaton restricts the possible switches from a given location to the next location, with a cost associated to each switch; the time interval between two consecutive switching times is greater than a fixed quantity. We show how a state-feedback solution can be computed off-line through a numerical procedure.

Optimal feedback switching laws for autonomous hybrid automata

We define a new class of hybrid systems called autonomous hybrid automata that can be seen as a generalization of the class of switched systems we have considered in previous works. In this new model there are two types of edges: a controllable edge represents a mode switch that can be triggered by the controller; an autonomous edge represents a mode switch that is triggered by the continuous state of the system as it reaches a given threshold. We show how to solve an infinite time horizon quadratic optimization problem with a numerically viable procedure for such a class of hybrid automata; the optimal control law is a state-feedback.

Optimal hybrid control for switched affine systems under safety and liveness constraints

In this contribution, we propose a two-level hierarchical control strategy to solve the problem of minimising a cost function for a switched affine system under safety and liveness constraints. The constraints are handled on the lower level by a discrete supervisory controller designed using l-complete approximation. Its action can be represented as state invariants added to the plant model. In a bottom-up strategy, we can then synthesis a high-level controller, which computes a set of switching tables using the remaining degrees of freedom to optimise a quadratic performance index

Quantized optimal control of discrete-time systems

In this paper we consider a quantized discrete-time linear quadratic regulator (DLQR) problem, namely a DLQR problem where the input u may only take values in a given finite set 14. Eased on our previous results on the optimal control of hybrid systems we show that the optimal control law for the quantized DLQR problem takes the form of a feedback control law, that can be obtained from a partition of the state space C, computed off-line. The numerical simulations carried out enabled us to observe a particular structure of C, related to the solution of the non-quantized DLQR problem. The lines of our future research in this topic are described in details in the last section, devoted to conclusions and future work

Observers for nondeterministic /spl lambda/-free labeled Petri nets

In this paper we deal with the problem of estimating the marking of a labeled Petri net with nondeterministic transitions. In particular, we consider the case in which nondeterminism is due to the presence of transitions that share the same label and that can be simultaneously enabled. Under the assumption that: the structure of the net is known, the initial marking is known, the transition labels can be observed, the nondeterministic transitions are contact-free, we present a technique for characterizing the set of markings that are consistent with the actual observation. More precisely, we show that the set of markings consistent with an observed word can be represented by a linear system with a fixed structure that does not depend on the length of the observed word.

State estimation and control of nondeterministic λ-free labeled petri nets

Abstract In this paper we present an original approach to estimate the marking of a labeled Petri net based on the observation of transition labels. In particular, we consider the case of nondeterministic transitions, i.e., transitions that share the same label and that can be simultaneously enabled. We also show how the estimate generated by the observer may be used to design a state feedback controller for forbidden marking specifications. More precisely, we discuss two different cases: the label-based feedback and the transition-based feedback, depending on the possibility of the controller to distinguish among transitions with the same label.