Peak estimation bounds extreme values of a function of state along trajectories of a dynamical system. This paper focuses on extending peak estimation to continuous and discrete settings with time-independent and time-dependent uncertainty. Techniques from optimal control are used to incorporate uncertainty into an existing occupation measure-based peak estimation framework, which includes special consideration for handling switching uncertainties. The resulting infinite-dimensional linear programs can be solved approximately with Linear Matrix Inequalities arising from the moment-SOS hierarchy.
Stability and $L_1/\ell_1$-to-$L_1/\ell_1$ performance analysis of uncertain impulsive linear positive systems with applications to the interval observation of impulsive and switched systems with constant delays
This paper is concerned with the problem of robust reliable control for a class of uncertain 2D discrete switched systems with state delays represented by a model of Roesser type. The parameter uncertainties are assumed to be norm-bounded. Firstly, delay-dependent sufficient condition for the exponential stability of the discrete 2D systems with state delays is established. Then, the concept of average dwell time is extended to 2D switched systems, and a reliable state feedback controller is developed in terms of linear matrix inequalities (LMIs) such that the resulting closed-loop system is e…
Cooperative Switched Formation Control of Autonomous Vehicles: An Event-triggered Approach to Input Saturation and Time-delay Challenges
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）；KTH Royal Institute of Technology（皇家理工学院）
Switched linear systems are time-varying nonlinear systems whose dynamics switch between different modes, where each mode corresponds to different linear dynamics. They arise naturally to model unexpected failures, environment uncertainties or system noises during system operation. In this paper, we consider a special class of switched linear systems where the mode switches are governed by Markov decision processes (MDPs). We study the problem of synthesizing a policy in an MDP that stabilizes the switched system. Given a policy, the switched linear system becomes a Markov jump linear system w…
This work provides a framework to compute an upper bound on the robust peak-to-peak gain of discrete-time uncertain linear systems using integral quadratic constraints (IQCs). Such bounds are of particular interest in the computation of reachable sets and the $\ell_1$-norm, as well as when safety-critical constraints need to be satisfied pointwise in time. The use of $ρ$-hard IQCs with a terminal cost enables us to deal with a wide variety of uncertainty classes, for example, we provide $ρ$-hard IQCs with a terminal cost for the class of parametric uncertainties. This approach unifies, general…
Peak estimation of hybrid systems aims to upper bound extreme values of a state function along trajectories, where this state function could be different in each subsystem. This finite-dimensional but nonconvex problem may be lifted into an infinite-dimensional linear program (LP) in occupation measures with an equal objective under mild finiteness/compactness and smoothness assumptions. This LP may in turn be approximated by a convergent sequence of upper bounds attained from solutions of Linear Matrix Inequalities (LMIs) using the Moment-Sum-of-Squares hierarchy. The peak estimation problem …
The adoption of containment measures to reduce the amplitude of the epidemic peak is a key aspect in tackling the rapid spread of an epidemic. Classical compartmental models must be modified and studied to correctly describe the effects of forced external actions to reduce the impact of the disease. The importance of social structure, such as the age dependence that proved essential in the recent COVID-19 pandemic, must be considered, and in addition, the available data are often incomplete and heterogeneous, so a high degree of uncertainty must be incorporated into the model from the beginnin…
