Discrete-time stability with perturbations: application to model predictive control
Automatica (Journal of IFAC)
Survey Constrained model predictive control: Stability and optimality
Automatica (Journal of IFAC)
Control of systems integrating logic, dynamics, and constraints
Automatica (Journal of IFAC)
Brief Equivalence of hybrid dynamical models
Automatica (Journal of IFAC)
On infinity norms as Lyapunov functions for piecewise affine systems
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
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In this paper we develop a priori stabilization conditions for infinity norm based hybrid MPC in the terminal cost and constraint set fashion. Closed-loop stability is achieved using infinity norm inequalities that guarantee that the value function corresponding to the MPC cost is a Lyapunov function of the controlled system. We show that Lyapunov asymptotic stability can be achieved even though the MPC value function may be discontinuous. One of the advantages of this hybrid MPC scheme is that the terminal constraint set can be directly obtained as a sublevel set of the calculated terminal cost, which is also a local piecewise linear Lyapunov function. This yields a new method to obtain positively invariant sets for PWA systems.