Scott A. Bortoff

Projection-free parallel quadratic programming for linear model predictive control

A key component in enabling the application of model predictive control (MPC) in fields such as automotive, aerospace, and factory automation is the availability of low-complexity fast optimisation algorithms to solve the MPC finite horizon optimal control problem in architectures with reduced computational capabilities. In this paper, we introduce a projection-free iterative optimisation algorithm and discuss its application to linear MPC. The algorithm, originally developed by Brand for non-negative quadratic programs, is based on a multiplicative update rule and it is shown to converge to a fixed point which is the optimum. An acceleration technique based on a projection-free line search is also introduced, to speed-up the convergence to the optimum. The algorithm is applied to MPC through the dual of the quadratic program (QP) formulated from the MPC finite time optimal control problem. We discuss how termination conditions with guaranteed degree of suboptimality can be enforced, and how the algorithm performance can be optimised by pre-computing the matrices in a parametric form. We show computational results of the algorithm in three common case studies and we compare such results with the results obtained by other available free and commercial QP solvers.

A Parallel Quadratic Programming Algorithm for Model Predictive Control

Abstract In this paper, an iterative multiplicative algorithm is proposed for the fast solution of quadratic programming (QP) problems that arise in the real-time implementation of Model Predictive Control (MPC). The proposed algorithm — Parallel Quadratic Programming ( PQP ) — is amenable to fine-grained parallelization. Conditions on the convergence of the PQP algorithm are given and proved. Due to its extreme simplicity, even serial implementations offer considerable speed advantages. To demonstrate, PQP is applied to several simulation examples, including a stand-alone QP problem and two MPC examples. When implemented in MATLAB using single-thread computations, numerical simulations of PQP demonstrate a 5 – 10x speed-up compared to the MATLAB active-set based QP solver quadprog. A parallel implementation would offer a further speed-up, linear in the number of parallel processors.

Optimal Codesign of Nonlinear Control Systems Based on a Modified Policy Iteration Method

This brief studies the optimal codesign of nonlinear control systems: simultaneous design of physical plants and related optimal control policies. Nonlinearity of the optimal codesign problem could come from either a nonquadratic cost function or the plant. After formulating the optimal codesign into a nonconvex optimization problem, an iterative scheme is proposed in this brief by adding an additional step of system-equivalence-based policy improvement to the conventional policy iteration. We have proved rigorously that the closed-loop system performance can be improved after each step of the proposed policy iteration scheme, and the convergence to a suboptimal solution is guaranteed. It is also shown that under certain conditions, this additional policy improvement step can be conducted by solving a quadratic programming problem. The linear version of the proposed methodology is addressed in the context of linear quadratic regulator. Finally, the effectiveness of the proposed methodology is illustrated through the optimal codesign of a load-positioning system.

On the optimal trajectory generation for servomotors: A Hamiltonian approach

This note considers the energy optimal trajectory generation of servo systems through open-loop optimal control design approach. Solving the exact optimal solution is challenging because of the nonlinear and switching cost function, and various constraints. The minimum principle is applied to establish piecewise necessary optimality conditions. An approximate optimal control is proposed to circumvent the difficulty due to the nonlinearity of the cost function. Simulation is performed to illustrate the generation of the approximate optimal trajectory.

An iterative approach to the optimal co-design of linear control systems

ABSTRACT This paper investigates the optimal co-design of both physical plants and control policies for a class of continuous-time linear control systems. The optimal co-design of a specific linear control system is commonly formulated as a nonlinear non-convex optimisation problem (NNOP), and solved by using iterative techniques, where the plant parameters and the control policy are updated iteratively and alternately. This paper proposes a novel iterative approach to solve the NNOP, where the plant parameters are updated by solving a standard semi-definite programming problem, with non-convexity no longer involved. The proposed system design is generally less conservative in terms of the system performance compared to the conventional system-equivalence-based design, albeit the range of applicability is slightly reduced. A practical optimisation algorithm is proposed to compute a sub-optimal solution ensuring the system stability, and the convergence of the algorithm is established. The effectiveness of the proposed algorithm is illustrated by its application to the optimal co-design of a physical load positioning system.

Coordinated Control of a Dual-Stage Positioning System Using Constrained Model Predictive Control

Dual-stage positioning systems have been widely used in factory automation, robotic manipulators, high-density data storage systems, and manufacturing systems. Trajectory generation and control of dual-stage positioning systems is of great importance and is made complicated by the presence of physical and operational constraints. In this work, we describe how to generate feasible reference trajectories for a dual-stage positioning system consisting of a fine stage and a coarse stage, and how to use them in a model predictive control algorithm for which recursive feasibility is guaranteed. The reference generation algorithm is guaranteed to generate trajectories that satisfy all the constraints for the fine and coarse stages. We also describe a constrained model predictive control algorithm used to control the coarse stage. The simulation results of applying the developed methodology to track a pre-determined pattern is presented.Copyright

Co-design of nonlinear control systems with bounded control inputs

This paper considers co-design of nonlinear constrained control systems: simultaneous design of the nonlinear plant and control policy where the control is bounded. Similar to prior art, the co-design is attacked as a non-convex optimization problem, which is solved by using an improved policy iteration scheme. We have proved rigorously that the system performance can be improved after each step of the proposed policy iteration scheme until convergence to a sub-optimal solution is attained. Effectiveness of the proposed methodology is illustrated through the co-design of a load-positioning system.

Exploiting refrigerant distribution for predictive control of multi-evaporator vapor compression systems

An observed behavior of refrigerant mass distribution in multi-path heat exchangers is exploited for control purposes. In this paper, we describe the following empirical property exploited for control: as the inlet valve position is decreased, refrigerant mass flow rate entering the heat exchanger is reduced, and for some flow rates, refrigerant is shown to preferentially flow in some paths more than others, causing maldistribution. This uneven refrigerant distribution is repeatable, reduces the capacity in a continuous manner and can be exploited with feedback controllers to regulate the perzone cooling. A controller is designed to provide stability and robustness to per-zone conditions and setpoints for this controller that relate per-path superheat temperature to overall evaporator capacity is created in such a way as to be robust to changes in local zone temperatures and the overall system evaporating temperature. This strategy provides zone decoupling and ultimately creates a virtual control input for a model predictive controller. Experiments demonstrate the effectiveness of this approach on a two-zone air conditioner in laboratory tests.

Model Predictive Control of Multi-zone Vapor Compression Systems

While the previous chapter presented modeling and control strategies for vapor compression systems in general, in this chapter, a model predictive controller is designed for a multi-zone vapor compression system. Controller requirements representing desired performance of production-scale equipment are provided and include baseline requirements common in control literature (constraint enforcement, reference tracking, disturbance rejection) and also extended requirements necessary for commercial application (selectively deactivating zones, implementable on embedded processors with limited memory/computation, compatibility with demand response events.). A controller architecture is presented based on model predictive control to meet the requirements. Experiments are presented validating constraint enforcement and automatic deactivation of zones.

From reeds-shepp's paths to continuous curvature paths-Part I: Transition schemes & algorithms

This work considers real-time continuous curvature (CC) path planning for car-like robots. It is motivated by the fact that Reeds-Shepps (RS) based path planning remains unmatched in terms of computation efficiency and reliability when compared with various CC path planning results. Similar to [1], this paper post-processes RS paths to enforce the CC property, while ensuring CC paths contained in a neighborhood of the RS paths to maintain obstacle clearance. Targeting to alleviate concerns about reliability and computational efficiency, we exploit the geometric insights casted by μ-tangency conditions [2] to post-process RS paths. Specifically, distinctive postprocessing scheme is devised offline for each type of discontinuous curvature junctions. The proposed schemes, though suboptimal, are straightforward, and result in CC path planning with guaranteed completeness at the negligible increase of computation. Effectiveness of proposed schemes and resultant algorithms is validated by numerical simulations.