A tractable approximation of chance constrained stochastic MPC based on affine disturbance feedback

This paper deals with model predictive control of uncertain linear discrete-time systems with polytopic constraints on the input and chance constraints on the states. When having polytopic constraints and bounded disturbances, the robust problem with an open-loop prediction formulation is known to be conservative. Recently, a tractable closed-loop prediction formulation was introduced, which can reduce the conservatism of the robust problem. We show that in the presence of chance constraints and stochastic disturbances, this closed-loop formulation can be used together with a tractable approximation of the chance constraints to further increase the performance while satisfying the chance constraints with the predefined probability

Least-restrictive robust periodic model predictive control applied to room temperature regulation

State-feedback model predictive control (MPC) of constrained discrete-time periodic affine systems is considered. The periodic systems’ states and inputs are subject to periodically time-dependent, hard, polyhedral constraints. Disturbances are additive, bounded and subject to periodically time-dependent bounds. The objective is to design MPC laws that robustly enforce constraint satisfaction in a manner that is least-restrictive, i.e., have the largest possible domain. The proposed design method is demonstrated on a building climate control example. The proposed method is directly applicable to time-invariant MPC

Least-restrictive robust MPC of periodic affine systems with application to building climate control

Robust state-feedback model predictive control (MPC) of discrete-time periodic affine systems is considered. States and inputs are subject to periodically time-dependent, hard, convex, polyhedral constraints. Disturbances are additive, bounded and subject to periodically time-dependent bounds. The control objective is given in terms of periodically time-dependent costs. First, maximum robust periodic controlled invariant sets are formally characterized and subsequently employed in the design of least-restrictive robustly strongly feasible periodic MPC problems. Finally, the proposed methods are applied to controlling room temperatures in buildings

Blocking parameterizations for improving the computational tractability of affine disturbance feedback MPC problems

Many model predictive control (MPC) schemes suffer from high computational complexity. Especially robust MPC schemes, which explicitly account for the effects of disturbances, can result in computationally intractable problems. So-called move-blocking is an effective method of reducing the computational complexity of MPC problems. Unfortunately move-blocking precludes the use of terminal constraints as a means of enforcing strong feasibility of MPC problems. Thus move-blocking MPC has traditionally been employed without rigorous guarantees of constraint satisfaction. A method for enforcing strong feasibility of nominal move-blocking MPC problems was recently developed. The contribution of this paper is to generalize this method and employ it for the purpose of enforcing strong feasibility of move-blocking affine disturbance feedback robust MPC problems. Furthermore the effectiveness of different disturbance-feedback blocking strategies is investigated by means of a numerical example

Strongly feasible stochastic model predictive control

In this article we develop a systematic approach to enforce strong feasibility of probabilistically constrained stochastic model predictive control problems for linear discrete-time systems under affine disturbance feedback policies. Two approaches are presented, both of which capitalize and extend the machinery of invariant sets to a stochastic environment. The first approach employs an invariant set as a terminal constraint, whereas the second one constrains the first predicted state. Consequently, the second approach turns out to be completely independent of the policy in question and moreover it produces the largest feasible set amongst all admissible policies. As a result, a trade-off between computational complexity and performance can be found without compromising feasibility properties. Our results are demonstrated by means of two numerical examples

Stochastic Model Predictive Control: Controlling the Average Number of Constraint Violations

This paper considers linear discrete-time systems with additive bounded disturbances subject to hard control input bounds and constraints on the expected number of state-constraint violations averaged over time, or, equivalently, constraints on the probability of a state-constraint violation averaged over time. This specification facilitates the exploitation of the information on the number of past constraint violations, and consequently enables a significant reduction in conservatism. For the type of constraint considered we develop a recursively feasible receding horizon scheme, and, as a simple modification of our approach, we show how a bound on the average number of violations can be enforced robustly. The computational complexity (online as well as offline) is comparable to existing model predictive control schemes. The effectiveness of the proposed methodology is demonstrated by means of a numerical example