Attaining mean square boundedness of a marginally stable noisy linear system with a bounded control input

We construct control policies that ensure bounded variance of a noisy marginally stable linear system in closed-loop. It is assumed that the noise sequence is a mutually independent sequence of random vectors, enters the dynamics affinely, and has bounded fourth moment. The magnitude of the control is required to be of the order of the first moment of the noise, and the policies we obtain are simple and computable.Comment: 10 page

On 1-norm stochastic optimal control with bounded control inputs

This paper deals with the finite horizon stochastic optimal control problem with the expectation of the 1-norm as the objective function and jointly Gaussian, although not necessarily independent, disturbances. We develop an approximation strategy that solves the problem in a certain class of nonlinear feedback policies, while ensuring satisfaction of hard input constraints. A bound on suboptimality of the proposed strategy in the class of aforementioned nonlinear feedback policies is given as well as a simple proof of mean-square stability of a receding horizon implementation provided that the system matrix is Schur stable

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

Stochastic receding horizon control with output feedback and bounded controls

International audienceWe study the problem of receding horizon control for stochastic discrete-time systems with bounded control inputs and incomplete state information. Given a suitable choice of causal control policies, we first present a slight extension of the Kalman filter to estimate the state optimally in mean-square sense. We then show how to augment the underlying optimization problem with a negative drift-like constraint, yielding a second-order cone program to be solved periodically online. We prove that the receding horizon implementation of the resulting control policies renders the state of the overall system mean-square bounded under mild assumptions. We also discuss how some quantities required by the finite-horizon optimization problem can be computed off-line, thus reducing the on-line computation

FeedNetBack - D05.04 - Design methodologies for event-based control systems

This is a Deliverable Report for the FeedNetBack project (www.feednetback.eu). Networked Control Systems (NCS) are systems in which the sensors or/and the actuators communicate with the controller through a network. Energy saving and robustness to unreliable channels are major challenges in networked control, notably in wireless scenarios. Energy efficiency and in particular asynchronous design methodologies are studied in this deliverable. The presence of a channel between the sensors measuring the plant and the controller generating the control inputs implies that the measurements should be quantized. As a preliminary step, the problem of finding a stabilizing policy with quantized measurements and bounded control inputs is considered. It is common to assume that the different nodes of a Network Control System use a periodic synchronized clock, this simplifies the model which may take into account some transmission delays. However, this assumption is strong and energy consuming. Indeed, the periodic sampling time is often chosen to ensure given performance in the worst case scenario, wasting energy when the system is running around its working point. To relax the assumption of synchronized nodes, the rest of the deliverable introduces two asynchronous design methodologies, event-based and self-triggered methodologies. The former consists in limiting the transmissions between the nodes when a given condition holds, or, in other words, when an event occurs. Not only this approach relaxes the assumption of synchronized nodes, but it also limits the transmissions which save energy. In the following, event-based approach is applied to a feedback control case and an estimation case. However, by its nature, event-based approach forces the communicating node to watch for the occurrence of the triggering event. This is relaxed in self-triggered approach where each node decides, at the end of an action (e.g. measuring, transmitting, controlling), when the next action will take place. In between these times, the node usually goes to down mode to save energy. In the last part of this deliverable, this approach is applied to a variable sample rate control and to the case of IEEE 802.15.4 protocol