An approach to output-feedback MPC of stochastic linear discrete-time systems

Abstract

In this paper we propose an output-feedback Model Predictive Control (MPC) algorithm for linear discrete-time systems affected by a possibly unbounded additive noise and subject to probabilistic constraints. In case the noise distribution is unknown, the probabilistic constraints on the input and state variables are reformulated by means of the Chebyshev -Cantelli inequality. The recursive feasibility is guaranteed, the convergence of the state to a suitable neighbor of the origin is proved under mild assumptions, and the implementation issues are thoroughly addressed. Two examples are discussed in details, with the aim of providing an insight into the performance achievable by the proposed control scheme.

Stochastic model predictive control with joint chance constraints

“…This can, however, potentially lead to a loss in control performance since the control policy u = v will not account for knowledge of future disturbances in the state prediction. To allow for handling hard input constraints in the presence of unbounded disturbances, the input constraints (2) can be relaxed in terms of expectation-type constraints [24] or chance constraints [9]. However, these approaches would not provide a rigorous guarantee for fulfillment of (2) with respect to all disturbance realizations.…”

“…Less suboptimal 1 SMPC formulations entail online computation of both the feedback control gains and the open-loop control actions. Such formulations, however, lead to a nonconvex optimization [9].…”

“…The problem setup considered in this paper is similar to that in [12,9]. Hard input constraints are relaxed to chance constraints in [9] to cope with the unbounded nature of disturbances, whereas the SMPC program presented in this work allows for directly handling the hard input constraints in an unbounded disturbance setting.…”

“…Hard input constraints are relaxed to chance constraints in [9] to cope with the unbounded nature of disturbances, whereas the SMPC program presented in this work allows for directly handling the hard input constraints in an unbounded disturbance setting. In addition, the SMPC approach in [9] results in a nonconvex program, which can become impractical for large-scale systems. On the other hand, the main contribution of this paper with respect to [12] is the ability to handle joint chance constraints while retaining the hard input constraints.…”

Hierarchical Model Predictive/Sliding Mode Control of Nonlinear Constrained Uncertain Systems

“…In addition, both the approaches are conservative, mainly because they (implicitly or explicitly) rely on worst-case techniques. If the uncertainties or the state and control disturbances are characterized as stochastic processes, the conservativeness of a deterministic worst case approach can be significantly reduced by the development of stochastic MPC algorithms with probabilistic state and/or input constraints (see [Farina et al, 2015] and the references therein reported).…”