Low-Rank Modifications of Riccati Factorizations for Model Predictive Control

In Model Predictive Control (MPC) the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem at each sample in the control loop. The main computational effort is often spent on computing the search directions, which in MPC corresponds to solving unconstrained finite-time optimal control (UFTOC) problems. This is commonly performed using Riccati recursions or generic sparsity exploiting algorithms. In this work the focus is efficient search direction computations for active-set (AS) type methods. The system of equations to be solved at each AS iteration is changed only by a low-rank modification of the previous one, and exploiting this structured change is important for the performance of AS type solvers. In this paper, theory for how to exploit these low-rank changes by modifying the Riccati factorization between AS iterations in a structured way is presented. A numerical evaluation of the proposed algorithm shows that the computation time can be significantly reduced by modifying, instead of re-computing, the Riccati factorization. This speed-up can be important for AS type solvers used for linear, nonlinear and hybrid MPC

Distributed eco-driving control of a platoon of electric vehicles through Riccati recursion

This paper presents a distributed optimization procedure for the cooperative eco-driving control problem of a platoon of electric vehiclessubject to safety and travel time constraints. Individual optimal trajectories are generated for each platoon member to account for heterogeneous vehicles and for the road slope. By rearranging the problem variables, the Riccati recursion can be applied along the chain-like structure of the platoon and be used to solve the problem by repeatedly transmitting information up and down the platoon. Since each vehicle is only responsible for its own part of the computations, the proposed control strategy is privacy-preserving and could therefore be deployed by any group of vehicles to form a platoon spontaneously while driving. The energy efficiency of this control strategy is evaluated in numerical experiments for platoons of electric trucks with different masses and rated motor powers

Linear estimation in Krein spaces. Part II. Applications

We have shown that several interesting problems in H∞-filtering, quadratic game theory, and risk sensitive control and estimation follow as special cases of the Krein-space linear estimation theory developed in Part I. We show that all these problems can be cast into the problem of calculating the stationary point of certain second-order forms, and that by considering the appropriate state space models and error Gramians, we can use the Krein-space estimation theory to calculate the stationary points and study their properties. The approach discussed here allows for interesting generalizations, such as finite memory adaptive filtering with varying sliding patterns

Distributed eco-driving control of a platoon of electric vehicles through Riccati recursion

This paper presents a distributed optimization procedure for the cooperative eco-driving control problem of a platoon of electric vehiclessubject to safety and travel time constraints. Individual optimal trajectories are generated for each platoon member to account for heterogeneous vehicles and for the road slope. By rearranging the problem variables, the Riccati recursion can be applied along the chain-like structure of the platoon and be used to solve the problem by repeatedly transmitting information up and down the platoon. Since each vehicle is only responsible for its own part of the computations, the proposed control strategy is privacy-preserving and could therefore be deployed by any group of vehicles to form a platoon spontaneously while driving. The energy efficiency of this control strategy is evaluated in numerical experiments for platoons of electric trucks with different masses and rated motor powers

A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process

We discuss a Krylov-Schur like restarting technique applied within the symplectic Lanczos algorithm for the Hamiltonian eigenvalue problem. This allows to easily implement a purging and locking strategy in order to improve the convergence properties of the symplectic Lanczos algorithm. The Krylov-Schur-like restarting is based on the SR algorithm. Some ingredients of the latter need to be adapted to the structure of the symplectic Lanczos recursion. We demonstrate the efficiency of the new method for several Hamiltonian eigenproblems

New optimization methods in predictive control

This thesis is mainly concerned with the efficient solution of a linear discrete-time finite horizon optimal control problem (FHOCP) with quadratic cost and linear constraints on the states and inputs. In predictive control, such a FHOCP needs to be solved online at each sampling instant. In order to solve such a FHOCP, it is necessary to solve a quadratic programming (QP) problem. Interior point methods (IPMs) have proven to be an efficient way of solving quadratic programming problems. A linear system of equations needs to be solved in each iteration of an IPM. The ill-conditioning of this linear system in the later iterations of the IPM prevents the use of an iterative method in solving the linear system due to a very slow rate of convergence; in some cases the solution never reaches the desired accuracy. A new well-conditioned IPM, which increases the rate of convergence of the iterative method is proposed. The computational advantage is obtained by the use of an inexact Newton method along with the use of novel preconditioners. A new warm-start strategy is also presented to solve a QP with an interior-point method whose data is slightly perturbed from the previous QP. The effectiveness of this warm-start strategy is demonstrated on a number of available online benchmark problems. Numerical results indicate that the proposed technique depends upon the size of perturbation and it leads to a reduction of 30-74% in floating point operations compared to a cold-start interior point method. Following the main theme of this thesis, which is to improve the computational efficiency of an algorithm, an efficient algorithm for solving the coupled Sylvester equation that arises in converting a system of linear differential-algebraic equations (DAEs) to ordinary differential equations is also presented. A significant computational advantage is obtained by exploiting the structure of the involved matrices. The proposed algorithm removes the need to solve a standard Sylvester equation or to invert a matrix. The improved performance of this new method over existing techniques is demonstrated by comparing the number of floating-point operations and via numerical examples