Soft constraints and penalty functions are commonly used in MPC to ensure that the optimization problem has a feasible solution, and thereby avoid MPC controller failure. On the other hand, soft constraints may allow for unnecessary violations of the original constraints, i.e., the constraints may be violated even if a valid solution that does not violate any constraints exists.
The paper develops procedures for the minimizing (according to some norm) of the Lagrange multipliers associated with a given mp-QP problem, assumed to originate from an MPC problem formulation. To this end the LICQ condition is exploited in order to efficiently formulate the optimization problem, and thereby improve upon existing mixed integer formulations and enhance the tractability of the problem. The results are used to design penalty functions such that corresponding soft constraints are made exact, that is, the original (hard) constraints are violated only if there exists no solution where all constraints are satisfied.
In this paper we provide a RPI over-approximation of the mRPI set associated for linear dynamics with zonotopic disturbances.We prove that the RPI construction converges toward the mRPI set and its conservatism diminishes monotonically with respect to the complexity of the representation (a “tightness” coefficient is calculated a priori). The results are tested in illustrative examples.
In the present paper we provide a robust approach for fault tolerant control (FTC) schemes using the methodology detailed in Seron et al. , Olaru et al. . We guarantee the detection and isolation of a fault through a set-separation condition (FDI mechanism) and use this condition further in the reconfiguration control (RC) mechanism in order to stabilize the closed-loop system and respect performance criteria.
In this paper we revisit the explicit MPC representation and related notions. We point to the special structure of the constraint matrices and exploit it in order to provide novel results. We give an upper bound for the collection of admissible active sets with use in the mixed integer representation of the KKT problem and a partial recursive description of the explicit partitioning of the MPC problem. The results are tested over illustrative examples.
A formulation of Persistently Exciting Model Predictive Control (PE-MPC) for Single-Input Single-Output (SISO) systems is presented. PE-MPC is an extension of a conventional model predictive control where a Persistence of Excitation Condition (PEC) is included as inequality constraint, to allow for adaptive implementation and on-line tuning of the model. The PEC makes the PE-MPC feasible region non-convex. For SISO systems the non-convex region can be represented as the union of two convex regions. Therefore an ad-hoc solution of the PE-MPC optimization problem can be eciently computed. This is done by exploiting the particular structure of the PEC constraint. Finally a numerical example of SISO sytem is given and several scenarios are simulated to analyze the PE-MPC properties.
In this paper we analyze the advantages of describing the constraint set of a constrained optimization problem by an (inner-approximating) zonotope. We compare this with the usual polytopic description and note that by using the generator description characterizing zonotopes we can exploit their special structure in order to obtain a simpler
formulation of the optimization problem. We test the results on a typical MPC setting and observe the improvements.