Stabilizing Stochastic Predictive Control under Bernoulli Dropouts

This article presents tractable and recursively feasible optimization-based controllers for stochastic linear systems with bounded controls. The stochastic noise in the plant is assumed to be additive, zero mean and fourth moment bounded, and the control values transmitted over an erasure channel. Three different transmission protocols are proposed having different requirements on the storage and computational facilities available at the actuator. We optimize a suitable stochastic cost function accounting for the effects of both the stochastic noise and the packet dropouts over affine saturated disturbance feedback policies. The proposed controllers ensure mean square boundedness of the states in closed-loop for all positive values of control bounds and any non-zero probability of successful transmission over a noisy control channel

Output feedback stable stochastic predictive control with hard control constraints

We present a stochastic predictive controller for discrete time linear time invariant systems under incomplete state information. Our approach is based on a suitable choice of control policies, stability constraints, and employment of a Kalman filter to estimate the states of the system from incomplete and corrupt observations. We demonstrate that this approach yields a computationally tractable problem that should be solved online periodically, and that the resulting closed loop system is mean-square bounded for any positive bound on the control actions. Our results allow one to tackle the largest class of linear time invariant systems known to be amenable to stochastic stabilization under bounded control actions via output feedback stochastic predictive control

Sparse and Constrained Stochastic Predictive Control for Networked Systems

This article presents a novel class of control policies for networked control of Lyapunov-stable linear systems with bounded inputs. The control channel is assumed to have i.i.d. Bernoulli packet dropouts and the system is assumed to be affected by additive stochastic noise. Our proposed class of policies is affine in the past dropouts and saturated values of the past disturbances. We further consider a regularization term in a quadratic performance index to promote sparsity in control. We demonstrate how to augment the underlying optimization problem with a constant negative drift constraint to ensure mean-square boundedness of the closed-loop states, yielding a convex quadratic program to be solved periodically online. The states of the closed-loop plant under the receding horizon implementation of the proposed class of policies are mean square bounded for any positive bound on the control and any non-zero probability of successful transmission

On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to a nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system

Optimal adaptive control for a class of stochastic systems

We study linear-quadratic adaptive tracking problems for a special class of stochastic systems expressed in the state-space form. This is a long-standing problem in the control of aircraft flying through atmospheric turbulence. Using an ELS-based algorithm and introducing dither in the control law we show that the resulting control achieves optimal cost in the limit, while simultaneously the unknown parameters converge to their true value