5 research outputs found
Stochastic Model Predictive Control with Discounted Probabilistic Constraints
This paper considers linear discrete-time systems with additive disturbances,
and designs a Model Predictive Control (MPC) law to minimise a quadratic cost
function subject to a chance constraint. The chance constraint is defined as a
discounted sum of violation probabilities on an infinite horizon. By penalising
violation probabilities close to the initial time and ignoring violation
probabilities in the far future, this form of constraint enables the
feasibility of the online optimisation to be guaranteed without an assumption
of boundedness of the disturbance. A computationally convenient MPC
optimisation problem is formulated using Chebyshev's inequality and we
introduce an online constraint-tightening technique to ensure recursive
feasibility based on knowledge of a suboptimal solution. The closed loop system
is guaranteed to satisfy the chance constraint and a quadratic stability
condition.Comment: 6 pages, Conference Proceeding
Stochastic MPC with Dynamic Feedback Gain Selection and Discounted Probabilistic Constraints
This paper considers linear discrete-time systems with additive disturbances,
and designs a Model Predictive Control (MPC) law incorporating a dynamic
feedback gain to minimise a quadratic cost function subject to a single chance
constraint. The feedback gain is selected from a set of candidates generated by
solutions of multiobjective optimisation problems solved by Dynamic Programming
(DP). We provide two methods for gain selection based on minimising upper
bounds on predicted costs. The chance constraint is defined as a discounted sum
of violation probabilities on an infinite horizon. By penalising violation
probabilities close to the initial time and ignoring violation probabilities in
the far future, this form of constraint allows for an MPC law with guarantees
of recursive feasibility without an assumption of boundedness of the
disturbance. A computationally convenient MPC optimisation problem is
formulated using Chebyshev's inequality and we introduce an online
constraint-tightening technique to ensure recursive feasibility. The closed
loop system is guaranteed to satisfy the chance constraint and a quadratic
stability condition. With dynamic feedback gain selection, the conservativeness
of Chebyshev's inequality is mitigated and closed loop cost is reduced with a
larger set of feasible initial conditions. A numerical example is given to show
these properties.Comment: 14 page