| Summary: | <p>Chance constraints, unlike robust constraints, allow constraint violation up to some predefined level and arise in numerous applications. They are often imposed in a pointwise-in-time fashion in control problems. This thesis considers a class of chance constraints imposed in an average-in-time fashion to focus more on aggregate behaviours and discounted to achieve trade-offs between short-term and long-term performance in the model predictive control (MPC) framework. </p>
<p>This thesis designs an MPC law for chance constrained stochastic systems with discrete-time linear dynamics and possibly unbounded additive disturbances.
The chance constraint is defined as a discounted sum of violation probabilities over an infinite horizon. By penalising violation probabilities close to the initial time and assigning violation probabilities in the far future with vanishingly small weights,
this form of constraints allows for an MPC law with guarantees of recursive feasibility by introducing an online constraint-tightening technique without an assumption of boundedness of the disturbance. We employ Chebyshev's inequality for constraint handling and formulate a computationally simple MPC optimisation problem. To mitigate the conservativeness of Chebyshev's inequality, a dynamic feedback gain is incorporated into the MPC law. This gain is selected online from a set of candidates generated by Pareto optimal solutions of a multiobjective optimisation problem.
The closed loop system is guaranteed to satisfy the chance constraint and a quadratic stability condition. With dynamic feedback gain selection, the closed loop cost is reduced and a larger set of feasible initial conditions is obtained. </p>
<p>This thesis also considers an application of stochastic MPC in networked control systems, where constrained linear systems are subject to stochastic additive disturbances and noisy measurements transmitted over a lossy communication channel. An MPC controller is designed to minimise a discounted cost subject to a discounted expectation constraint. Sensor data is assumed to be lost with a known probability. Data losses are accounted for by expressing the predicted control policy as an affine function of future observations, resulting in a convex optimal control problem. Recursive feasibility of online optimisation problems and constraint satisfaction are ensured similarly via the constraint-tightening technique. We show that the discounted cost evaluated along trajectories of the closed loop system is bounded. Under certain conditions, the averaged undiscounted closed loop cost accumulated over an infinite horizon also remains bounded.</p>
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