Risk-sensitive optimal feedback control accounts for sensorimotor behavior under uncertainty

Many aspects of human motor behavior can be understood using optimality principles such as optimal feedback control. However, these proposed optimal control models are risk-neutral; that is, they are indifferent to the variability of the movement cost. Here, we propose the use of a risk-sensitive optimal controller that incorporates movement cost variance either as an added cost (risk-averse controller) or as an added value (risk-seeking controller) to model human motor behavior in the face of uncertainty. We use a sensorimotor task to test the hypothesis that subjects are risk-sensitive. Subjects controlled a virtual ball undergoing Brownian motion towards a target. Subjects were required to minimize an explicit cost, in points, that was a combination of the final positional error of the ball and the integrated control cost. By testing subjects on different levels of Brownian motion noise and relative weighting of the position and control cost, we could distinguish between risk-sensitive and risk-neutral control. We show that subjects change their movement strategy pessimistically in the face of increased uncertainty in accord with the predictions of a risk-averse optimal controller. Our results suggest that risk-sensitivity is a fundamental attribute that needs to be incorporated into optimal feedback control models. © 2010 Nagengast et al.

Hybrid model predictive control applied to switching control of burner load for a compact marine boi

This paper discusses the application of hybrid model predictive control to control switching between different burner modes in a novel compact marine boiler design. A further purpose of the present work is to point out problems with finite horizon model predictive control applied to systems for which the optimal solution is a limit cycle. Regarding the marine boiler control the aim is to find an optimal control strategy which minimizes a trade-off between deviations in boiler pressure and water level from their respective setpoints while limiting burner switches.The approach taken is based on the Mixed Logic Dynamical framework. The whole boiler systems is modelled in this framework and a model predictive controller is designed. However to facilitate on-line implementation only a small part of the search tree in the mixed integer optimization is evaluated to find out whether a switch should occur or not. The strategy is verified on a simulation model of the compact marine boiler for control of low/high burner load switches. It is shown that even though performance is adequate for some disturbance levels it becomes deteriorated when the optimal solution is a limit cycle. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.

Active control of high-frequency vibration: Optimisation using the hybrid modelling method

This work presents active control of high-frequency vibration using skyhook dampers. The choice of the damper gain and its optimal location is crucial for the effective implementation of active vibration control. In vibration control, certain sensor/actuator locations are preferable for reducing structural vibration while using minimum control effort. In order to perform optimisation on a general built-up structure to control vibration, it is necessary to have a good modelling technique to predict the performance of the controller. The present work exploits the hybrid modelling approach, which combines the finite element method (FEM) and statistical energy analysis (SEA) to provide efficient response predictions at medium to high frequencies. The hybrid method is implemented here for a general network of plates, coupled via springs, to allow study of a variety of generic control design problems. By combining the hybrid method with numerical optimisation using a genetic algorithm, optimal skyhook damper gains and locations are obtained. The optimal controller gain and location found from the hybrid method are compared with results from a deterministic modelling method. Good agreement between the results is observed, whereas results from the hybrid method are found in a significantly reduced amount of time. © 2012 Elsevier Ltd. All rights reserved.

LQ optimal and risk-sensitive control for vehicle suspensions

This paper is concerned with time-domain optimal control of active suspensions. The optimal control problem formulation has been generalised by incorporating both road disturbances (ride quality) and a representation of driver inputs (handling quality) into the optimal control formulation. A regular optimal control problem as well as a risk-sensitive exponential optimal control performance index is considered. Emphasis has been given to practical considerations including the issue of state estimation in the presence of load disturbances (driver inputs). © 2012 IEEE.

Antiwindup design for induction motor control in the field weakening domain

Operation of induction machines in the high-speed and/or high-torque range requires field-weakening to comply with voltage and current physical limitations. This paper presents an anti-windup approach to this problem: rather than developing an ad-hoc field weakening strategy in the high-speed region, we equip an unconstrained vector-control design with an anti-windup module that automatically adjusts the current and flux set-points so that voltage and current constraints are satisfied at every operating point. The anti-windup module includes a feedforward modification of the set point aimed at maximizing the available torque in steady-state and a feedback modification of the controller based on an internal model-based antiwindup scheme. This paper includes a complete stability analysis of the proposed solution and presents encouraging experimental results on an industrial drive. © 2012 IEEE.

Model based control for closed loop testing of 1-D engine simulation models

1-D engine simulation models are widely used for the analysis and verification of air-path design concepts and prediction of the resulting engine transient response. The latter often requires closed loop control over the model to ensure operation within physical limits and tracking of reference signals. For this purpose, a particular implementation of Model Predictive Control (MPC) based on a corresponding Mean Value Engine Model (MVEM) is reported here. The MVEM is linearised on-line at each operating point to allow for the formulation of quadratic programming (QP) problems, which are solved as the part of the proposed MPC algorithm. The MPC output is used to control a 1-D engine model. The closed loop performance of such a system is benchmarked against the solution of a related optimal control problem (OCP). As an example this study is focused on the transient response of a light-duty car Diesel engine. For the cases examined the proposed controller implementation gives a more systematic procedure than other ad-hoc approaches that require considerable tuning effort. © 2012 IFAC.

Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.

Computational approaches to motor control.

This review will focus on four areas of motor control which have recently been enriched both by neural network and control system models: motor planning, motor prediction, state estimation and motor learning. We will review the computational foundations of each of these concepts and present specific models which have been tested by psychophysical experiments. We will cover the topics of optimal control for motor planning, forward models for motor prediction, observer models of state estimation arid modular decomposition in motor learning. The aim of this review is to demonstrate how computational approaches, as well as proposing specific models, provide a theoretical framework to formalize the issues in motor control.

A hybrid systems approach to trajectory tracking control for juggling systems

From a hybrid systems point of view, we provide a modeling framework and a trajectory tracking control design methodology for juggling systems. We present the main ideas and concepts in a one degree-of-freedom juggler, which consists of a ball bouncing on an actuated robot. We design a hybrid control strategy that, with only information of the ball's state at impacts, controls the ball to track a reference rhythmic pattern with arbitrary precision. We extend this hybrid control strategy to the case of juggling multiple balls with different rhythmic patterns. Simulation results for juggling of one and three balls with a single actuated robot are presented. © 2007 IEEE.

CLF based designs with robustness to dynamic input uncertainties

The problem of robust stabilization of nonlinear systems in the presence of input uncertainties is of great importance in practical implementation. Stabilizing control laws may not be robust to this type of uncertainty, especially if cancellation of nonlinearities is used in the design. By exploiting a connection between robustness and optimality, "domination redesign" of the control Lyapunov function (CLF) based Sontag's formula has been shown to possess robustness to static and dynamic input uncertainties. In this paper we provide a sufficient condition for the domination redesign to apply. This condition relies on properties of local homogeneous approximations of the system and of the CLF. We show that an inverse optimal control law may not exist when these conditions are violated and illustrate how these conditions may guide the choice of a CLF which is suitable for domination redesign. © 1999 Elsevier Science B.V. All rights reserved.

Stability margins of nonlinear receding-horizon control via inverse optimality

Using the nonlinear analog of the Fake Riccati equation developed for linear systems, we derive an inverse optimality result for several receding-horizon control schemes. This inverse optimality result unifies stability proofs and shows that receding-horizon control possesses the stability margins of optimal control laws. © 1997 Elsevier Science B.V.

Finite horizon LQR control with limited controller-system communication

We consider finite-horizon LQR control with limited controller-system communication. Within a time-horizon T , the controller can only communicate with the system doptimal control data schedule for unstable first-order systems and a class of higher-order systems. We also discuss when such a control data schedule remains optimal (or is near optimal) for general systems. © 1963-2012 IEEE.

Field programmable gate array based predictive control system for spacecraft rendezvous in elliptical orbits

Copyright © 2014 John Wiley & Sons, Ltd. Copyright © 2014 John Wiley & Sons, Ltd. Summary A field programmable gate array (FPGA) based model predictive controller for two phases of spacecraft rendezvous is presented. Linear time-varying prediction models are used to accommodate elliptical orbits, and a variable prediction horizon is used to facilitate finite time completion of the longer range manoeuvres, whilst a fixed and receding prediction horizon is used for fine-grained tracking at close range. The resulting constrained optimisation problems are solved using a primal-dual interior point algorithm. The majority of the computational demand is in solving a system of simultaneous linear equations at each iteration of this algorithm. To accelerate these operations, a custom circuit is implemented, using a combination of Mathworks HDL Coder and Xilinx System Generator for DSP, and used as a peripheral to a MicroBlaze soft-core processor on the FPGA, on which the remainder of the system is implemented. Certain logic that can be hard-coded for fixed sized problems is implemented to be configurable online, in order to accommodate the varying problem sizes associated with the variable prediction horizon. The system is demonstrated in closed-loop by linking the FPGA with a simulation of the spacecraft dynamics running in Simulink on a PC, using Ethernet. Timing comparisons indicate that the custom implementation is substantially faster than pure embedded software-based interior point methods running on the same MicroBlaze and could be competitive with a pure custom hardware implementation.