Claus Danielson

Symmetric Linear Model Predictive Control

This paper studies symmetry in linear model predictive control (MPC). We define symmetry for model predictive control laws and for model predictive control problems. Properties of both MPC symmetries are studied by using a group theory formalism. We show how to efficiently compute MPC symmetries by transforming the search of MPC symmetry generators into a graph automorphism problem. MPC symmetries are then used to design model predictive control algorithms with reduced complexity. The effectiveness of the proposed approach is shown through a simple large-scale MPC problem whose explicit solution can only be found with the method presented in this paper.

A reconfigurable Plug-and-Play Model Predictive Controller for multi-evaporator vapor compression systems

This paper presents a reconfigurable Plug-and-Play (PnP) Model Predictive Controller (MPC) for multi-evaporator vapor compression systems (VCS) where individual evaporators are permitted to turn on or off. This alters the number of performance variables, actuators and constraints. The proposed approach features structural online updates of the closed loop system with stability guarantees, and avoids the need to commission and tune separate controllers for when individual subsystems are turned on or off. To compare the performance of the proposed approach, a more conventional switched MPC is also developed in order to provide a benchmark design, wherein separate model representations are developed and controllers with numerous tuning parameters are synthesized and deployed depending on the VCS operation mode. Simulations are provided comparing the performance of the proposed reconfigurable PnP MPC to the traditionally-designed switched MPC. Results confirm that the reconfigurable PnP MPC maintains the same performance as the switched MPC approach in terms of room temperature reference tracking after zones are switched on, enforcement of critical machine constraints, and disturbance rejection. However, reconfigurable PnP MPC requires no extra tuning or controller design effort, and can be automatically synthesized from a single master controller design for any VCS operating mode.

Path planning using positive invariant sets

We present an algorithm for steering the output of a linear system from a feasible initial condition to a desired target position, while satisfying input constraints and nonconvex output constraints. The system input is generated by a collection of local linear state-feedback controllers. The path-planning algorithm selects the appropriate local controller using a graph search, where the nodes of the graph are the local controllers and the edges of the graph indicate when it is possible to transition from one local controller to another without violating input or output constraints. We present two methods for computing the local controllers. The first uses a fixed-gain controller and scales its positive invariant set to satisfy the input and output constraints. We provide a linear program for determining the scale-factor and a condition for when the linear program has a closed-form solution. The second method designs the local controllers using a semi-definite program that maximizes the volume of the positive invariant set that satisfies state and input constraints. We demonstrate our path-planning algorithm on docking of a spacecraft. The semi-definite programming based control design has better performance but requires more computation.

Stability and feasibility of MPC for switched linear systems with dwell-time constraints

This paper considers the control of discrete-time switched linear systems using model predictive control. A model predictive controller is designed with terminal cost and constraints depending on the terminal mode of the switched linear system. Conditions on the terminal cost and constraints are presented to ensure persistent feasibility and stability of the closed-loop system given sufficiently long dwell-time. A procedure is proposed to numerically compute admissible terminal costs and constraint sets.

Reconfigurable Model Predictive Control for Multievaporator Vapor Compression Systems

This paper considers the control of a multievaporator vapor compression system (ME-VCS) where individual evaporators are permitted to turn ON or OFF. We present a model predictive controller (MPC) that can be easily reconfigured for different ON/OFF configurations of the system. In this approach, only the cost function of the constrained finite-time optimal control problem is updated depending on the system configuration. Exploiting the structure of the system dynamics, the cost function is modified by zeroing elements of the state, input, and terminal cost matrices. The advantage of this approach is that cost matrices for each configuration of the ME-VCS do not need to be stored or computed online. This reduces the effort required to tune and calibrate the controller and the amount of memory required to store the controller parameters in a microprocessor. The reconfigurable MPC is compared with a conventional approach in which individual model predictive controllers are independently designed for each ON/OFF configuration. The simulations show that the reconfigurable MPC method provides a similar closed-loop performance in terms of reference tracking and constraint satisfaction to the set of individual model predictive controllers. Further, we show that our controller requires substantially less memory than the alternative approaches. Experiments on a residential two-zone vapor compression system further validate the reconfigurable MPC method.

Model predictive control for treating cancer with ultrasonic heating

This paper investigates thermal ablation of cancer tissue as a controls problem. The objective is to deliver a lethal dose of thermal energy to the cancer tissue without damaging critical nearby healthy tissue. This paper proposes a model predictive controller (MPC) to regulate thermal dose. The model predictive controller guarantees the safety of the healthy tissue surrounding the tumor. The cost function rewards killing cancer cells. Simulations comparing the proposed controller with the bang-bang controller used in practice demonstrate that the MPC controller kills more of the cancer tissue and requires less time than the bang-bang controller, while damaging less healthy tissue.

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.

Indirect adaptive MPC for output tracking of uncertain linear polytopic systems

We present an indirect adaptive model predictive control algorithm for output tracking of linear systems with polytopic uncertainty. The proposed approach is based on the velocity form of the system model, and achieves input-to-state stable output tracking with respect to the parameter estimation error and the rate of change of time-varying references. For the constrained case, recursive feasibility is achieved by including robust constraints designed from a robust control invariant set for the system model, and terminal constraints designed from a positive invariant set for the velocity model. Simulation results for a numerical example and an air conditioning control application demonstrate the method.

Symmetric Control Design for Multi-Evaporator Vapor Compression Systems

Multi-evaporator vapor compression systems (ME-VCS) are inherently multiinput multioutput (MIMO) systems, often with complex, highly coupled dynamics. Thus, they require more sophisticated control schemes than traditional on-off logic, or decentralized proportionalintegral controllers. Unfortunately, many MIMO control design techniques are not well suited for this problem since they require complex numerical computations that do not scale gracefully for the high-dimensional dynamics of ME-VCS systems. This paper exploits the observed similarity of the room dynamics to reduce the computational complexity of designing controllers. We use a linear matrix inequality based controller synthesis technique that exploits symmetry for designing controllers for large-scale ME-VCS systems. This controller synthesis technique was applied to an MEVCS system with 50 rooms. Using tradition control design methods required 41 hours to synthesize a controller, while our technique designed an identical controller in less than 1 second. ASME Dynamic Systems and Control Conference This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c

Motion planning with invariant set trees

This paper introduces the planning algorithm Sa-feRRT, which extends the rapidly-exploring random tree (RRT) algorithm by using feedback control and positively invariant sets to guarantee collision-free closed-loop path tracking. The SafeRRT algorithm steers the output of a system from a feasible initial value to a desired goal, while satisfying input constraints and non-convex output constraints. The algorithm constructs a tree of local state-feedback controllers, each with a randomly sampled reference equilibrium and corresponding positively invariant set. The positively invariant sets indicate when it is possible to safely transition from one local controller to another without violating constraints. The tree is expanded from the desired goal until it contains the initial condition, at which point traversing the tree yields a dynamically feasible and safe closed-loop trajectory. We demonstrate SafeRRT on a spacecraft rendezvous example.