Publication

Robust stability properties of soft constrained MPC

Colin Neil Jones, Melanie Nicole Zeilinger
2010
Conference Papers

Abstract

In Model Predictive Control, the enforcement of hard state constraints can be overly conservative or even infeasible, especially in the presence of disturbances. This work presents a soft constrained MPC approach that provides closed- loop stability even for unstable systems. Two types of soft constraints are employed: state constraints along the horizon are relaxed by the introduction of two different types of slack variables and the terminal constraint is softened by moving the target from the origin to a feasible steady-state. The proposed method significantly enlarges the region of attraction and preserves the optimal behavior whenever all state constraints can be enforced. Asymptotic stability of the nominal system under the proposed control law is shown, as well as input-to- state stability of the system under additive disturbances and the robust stability properties are analyzed.

Official source

https://infoscience.epfl.ch/entities/publication/3eab48e4-51f2-4393-a33f-c6edbe25e27a

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Colin Neil Jones, Melanie Nicole Zeilinger
2010
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/3eab48e4-51f2-4393-a33f-c6edbe25e27a

About this result

Related concepts (32)

Lyapunov stability

Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis).

Constraint (mathematics)

In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set. The following is a simple optimization problem: subject to and where denotes the vector (x1, x2). In this example, the first line defines the function to be minimized (called the objective function, loss function, or cost function).

Marginal stability

In the theory of dynamical systems and control theory, a linear time-invariant system is marginally stable if it is neither asymptotically stable nor unstable. Roughly speaking, a system is stable if it always returns to and stays near a particular state (called the steady state), and is unstable if it goes farther and farther away from any state, without being bounded. A marginal system, sometimes referred to as having neutral stability, is between these two types: when displaced, it does not return to near a common steady state, nor does it go away from where it started without limit.

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Robust stability properties of soft constrained MPC

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