Domenico Mignone

Stability and stabilization of piecewise affine and hybrid systems: an LMI approach

In this paper we present various algorithms both for stability analysis and state-feedback design for discrete-time piecewise affine systems. Our approach hinges on the use of piecewise quadratic Lyapunov functions that can be computed as the solution of a set of linear matrix inequalities. We show that the continuity of the Lyapunov function is not required in the discrete-time case. Moreover, the basic algorithms are made less conservative by exploiting the switching structure of piecewise affine systems and by using relaxation procedures.

Moving horizon estimation for hybrid systems

We propose a state-smoothing algorithm for hybrid systems based on moving-horizon estimation (MHE) by exploiting the equivalence between hybrid systems modeled in the mixed logic dynamical form and piecewise affine systems. We provide sufficient conditions on the time horizon and the penalties on the state at the beginning of the estimation horizon to guarantee asymptotic convergence of the MHE scheme. Moreover, we propose two practical algorithms for the computation of penalties that allow us to implement MHE by solving a mixed-integer quadratic program.

Moving horizon estimation for hybrid systems and fault detection

An approach for fault detection and state estimation of hybrid systems is presented. The method relies on the modeling framework for hybrid systems introduced by Bemporad and Morari (1999). This framework considers interacting propositional logic, automata, continuous dynamics and constraints. The proposed approach is illustrated by considering the fault detection problem of the three-tank benchmark system.

A framework for control, fault detection, state estimation, and verification of hybrid systems

This paper presents a modeling formalism for hybrid systems which allows one to formulate and solve several practical problems, such as control, formal verification, state estimation, and fault detection. As an extension to previous works we report a technique that allows one to reduce the number of auxiliary binary variables in the modeling phase.

Analysis and control with performance of piecewise affine and hybrid systems

In this paper we investigate some analysis and control problems with performance for discrete-time hybrid systems in the piecewise affine form. By using arguments from the dissipativity theory for nonlinear systems, we show that H/sub /spl infin// analysis and synthesis problems can be formulated and solved via linear matrix inequalities that take into account the switching structure of the systems. Moreover, such procedures can be generalized in order to solve both robust control problems and analysis/synthesis with other performance indices like the generalized H/sub 2/ norm.

Reconfiguration strategies for hybrid systems

In this work we propose several algorithms to solve the reconfiguration problem for linear and hybrid systems. In particular, we consider the decision about the usage of redundant hardware in order to compensate for faults. While this problem can be translated into a constrained model predictive control framework, the computational complexity grows very fast, as the number of possible decisions increases. In this work we propose schemes, that require low computational effort. We discuss the applicability of the methods considering the reconfiguration of the three tank benchmark system.

A Framework for Control, State Estimation, Fault Detection, and Verification of Hybrid Systems

Mixed Logic Dynamical (MLD) systems were introduced as a new system type by the authors recently. The MLD form is capable to model a broad class of systems arising in many applications, among them: linear hybrid systems; sequential logical systems (finite state machines, automata); piecewise linear systems. The paper reviews this modeling paradigm and gives an overview of the many control related problems (optimal feedback, estimation, fault detection) which can be formulated and solved in this framework. Generally, the on-line solution of Mixed-Integer Linear Programs or Mixed-Integer Quadratic Programs is required. Strategic formulations and taylored search procedures are proposed, so that this task should be feasible for problems of reasonable size.