A Sub-optimal Algorithm to Synthesize Control Laws for a Network of Dynamic Agents

We study the synthesis problem of an LQR controller when the matrix describing the control law is constrained to lie in a particular vector space. Our motivation is the use of such control laws to stabilize networks of autonomous agents in a decentralized fashion; with the information flow being dictated by the constraints of a pre-specified topology. In this paper, we consider the finite-horizon version of the problem and provide both a computationally intensive optimal solution and a sub-optimal solution that is computationally more tractable. Then we apply the technique to the decentralized vehicle formation control problem and show that the loss in performance due to the use of the sub-optimal solution is not huge; however the topology can have a large effect on performance

Move blocking strategies in receding horizon control

Abstract — In order to deal with the computational burden of optimal control, it is common practice to reduce the degrees of freedom by fixing the input or its derivatives to be constant over several time-steps. This policy is referred to as “move blocking”. This paper will address two issues. First, a survey of various move blocking strategies is presented and the shortcomings of these blocking policies, such as the lack of stability and constraint satisfaction guarantees, will be illustrated. Second, a novel move blocking scheme, “Moving Window Blocking” (MWB), will be presented. In MWB, the blocking strategy is time-dependent such that the scheme yields stability and feasibility guarantees for the closed-loop system. Finally, the results of a large case-study are presented that illustrate the advantages and drawbacks of the various control strategies discussed in this paper

Conjectures on an algorithm for convex parametric quadratic programs

An algorithm for convex parametric QPs is studied. The algorithm explores the parameter space by stepping a sufficiently small distance over the facets of each critical region and thereby identifying the neighboring regions. Some conjectures concerning this algorithm and the structure of the solution of a parametric QP are presented

On the facet-to-facet property of solutions to convex parametric quadratic programs

In some of the recently developed algorithms for convex parametric quadratic programs it is implicitly assumed that the intersection of the closures of two adjacent critical regions is a facet of both closures; this will be referred to as the facet-to-facet property. It is shown by an example, whose solution is unique, that the facet-to-facet property does not hold in general. Consequently, some existing algorithms cannot guarantee that the entire parameter space will be explored. A simple modification, applicable to several existing algorithms, is presented for the purpose of overcoming this problem. Numerical results indicate that, compared to the original algorithms for parametric quadratic programs, the proposed method has lower computational complexity for problems whose solutions consist of a large number of critical regions

Multiparametric Linear Complementarity Problems

The linear complementarity problem (LCP) is a general problem that unifies linear and quadratic programs and bimatrix games. In this paper, we present an efficient algorithm for the solution to multiparametric linear complementarity problems (pLCPs) that are defined by positive semi-definite matrices. This class of problems includes the multiparametric linear (pLP) and semi-definite quadratic programs (pQP), where parameters are allowed to appear linearly in the cost and the right hand side of the constraints. We demonstrate that the proposed algorithm is equal in efficiency to the best of current pLP and pQP solvers for all problems that they can solve, and yet extends to a much larger clas

Model Predictive Control of an Underactuated Spacecraft with Two Reaction Wheels

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143105/1/1.G000320.pd