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.

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.

Fault-tolerant model predictive control of a wind turbine benchmark

This paper aims to solve the fault tolerant control problem of a wind turbine benchmark. A hierarchical controller with model predictive pre-compensators, a global model predictive controller and a supervisory controller is proposed. In the model predictive pre-compensator, an extended Kalman Filter is designed to estimate the system states and various fault parameters. Based on the estimation, a group of model predictive controllers are designed to compensate the fault effects for each component of the wind turbine. The global MPC is used to schedule the operation of the components and exploit potential system-level redundancies. Extensive simulations of various fault conditions show that the proposed controller has small transients when faults occur and uses smoother and smaller generator torque and pitch angle inputs than the default controller. This paper shows that MPC can be a good candidate for fault tolerant controllers, especially the one with an adaptive internal model combined with a parameter estimation and update mechanism, such as an extended Kalman Filter. © 2012 IFAC.

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.

Minimum maneuver time calculation using convex optimization

The problem of calculating the minimum lap or maneuver time of a nonlinear vehicle, which is linearized at each time step, is formulated as a convex optimization problem. The formulation provides an alternative to previously used quasi-steady-state analysis or nonlinear optimization. Key steps are: the use of model predictive control; expressing the minimum time problem as one of maximizing distance traveled along the track centerline; and linearizing the track and vehicle trajectories by expressing them as small displacements from a fixed reference. A consequence of linearizing the vehicle dynamics is that nonoptimal steering control action can be generated, but attention to the constraints and the cost function minimizes the effect. Optimal control actions and vehicle responses for a 90 deg bend are presented and compared to the nonconvex nonlinear programming solution. Copyright © 2013 by ASME.

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.

H∞ sampled-data synthesis and related numerical issues

In this paper we present a new, compact derivation of state-space formulae for the so-called discretisation-based solution of the H∞ sampled-data control problem. Our approach is based on the established technique of continuous time-lifting, which is used to isometrically map the continuous-time, linear, periodically time-varying, sampled-data problem to a discretetime, linear, time-invariant problem. State-space formulae are derived for the equivalent, discrete-time problem by solving a set of two-point, boundary-value problems. The formulae accommodate a direct feed-through term from the disturbance inputs to the controlled outputs of the original plant and are simple, requiring the computation of only a single matrix exponential. It is also shown that the resultant formulae can be easily re-structured to give a numerically robust algorithm for computing the state-space matrices. © 1997 Elsevier Science Ltd. All rights reserved.

Bypass transition to sustained thermoacoustic oscillations in a linearly stable rijke tube

In this paper we examine triggering in a simple linearly-stable thermoacoustic system using techniques from flow instability and optimal control. Firstly, for a noiseless system, we find the initial states that have highest energy growth over given times and from given energies. Secondly, by varying the initial energy, we find the lowest energy that just triggers to a stable periodic solution. We show that the corresponding initial state grows first towards an unstable periodic solution and, from there, to the stable periodic solution. This exploits linear transient growth, which arises due to nonnormality in the governing equations and is directly analogous to bypass transition to turbulence. Thirdly, we introduce noise that has similar spectral characteristics to this initial state. We show that, when triggering from low noise levels, the system grows to high amplitude self-sustained oscillations by first growing towards the unstable periodic solution of the noiseless system. This helps to explain the experimental observation that linearly-stable systems can trigger to self-sustained oscillations even with low background noise. © 2010 by University of Cambridge. Published by the American Institute of Aeronautics and Astronautics, Inc.

Measurement-Integrated simulations and Kalman filter applied to a co-flowing jet

This paper deals with the experimental evaluation of a flow analysis system based on the integration between an under-resolved Navier-Stokes simulation and experimental measurements with the mechanism of feedback (referred to as Measurement-Integrated simulation), applied to the case of a planar turbulent co-flowing jet. The experiments are performed with inner-to-outer-jet velocity ratio around 2 and the Reynolds number based on the inner-jet heights about 10000. The measurement system is a high-speed PIV, which provides time-resolved data of the flow-field, on a field of view which extends to 20 jet heights downstream the jet outlet. The experimental data can thus be used both for providing the feedback data for the simulations and for validation of the MI-simulations over a wide region. The effect of reduced data-rate and spatial extent of the feedback (i.e. measurements are not available at each simulation time-step or discretization point) was investigated. At first simulations were run with full information in order to obtain an upper limit of the MI-simulations performance. The results show the potential of this methodology of reproducing first and second order statistics of the turbulent flow with good accuracy. Then, to deal with the reduced data different feedback strategies were tested. It was found that for small data-rate reduction the results are basically equivalent to the case of full-information feedback but as the feedback data-rate is reduced further the error increases and tend to be localized in regions of high turbulent activity. Moreover, it is found that the spatial distribution of the error looks qualitatively different for different feedback strategies. Feedback gain distributions calculated by optimal control theory are presented and proposed as a mean to make it possible to perform MI-simulations based on localized measurements only. So far, we have not been able to low error between measurements and simulations by using these gain distributions.

Verifying stability of approximate explicit MPC

Several authors have proposed algorithms for approximate explicit MPC [1],[2],[3]. These algorithms have in common that they develop a stability criterion for approximate explicit MPC that require the approximate cost function to be within a certain distance from the optimal cost function. In this paper, stability is instead ascertained by considering only the cost function of the approximate MPC. If a region of the state space is found where the cost function is not decreasing, this indicates that an improved approximation (to the optimal control) is required in that region. If the approximate cost function is decreasing everywhere, no further refinement of the approximate MPC is necessary, since stability is guaranteed. ©2009 IEEE.

Robust multiplexed MPC for distributed multi-agent systems

This paper extends the authors' earlier work which adapted robust multiplexed MPC for application to distributed control of multi-agent systems with non-interacting dynamics and coupled constraint sets in the presence of persistent unknown, but bounded disturbances. Specifically, we propose exploiting the single agent update nature of the multiplexed approach, and fix the update sequence to enable input move-blocking and increased discretisation rates. This permits a higher rate of individual policy update to be achieved, whilst incurring no additional computational cost in the corresponding optimal control problems to be solved. A disturbance feedback policy is included between updates to facilitate finding feasible solutions. The new formulation inherits the property of rapid response to disturbances from multiplexing the control and numerical results show that fixing the update sequence does not incur any loss in performance. © 2011 IFAC.

Lyapunov theory for zeno stability

Zeno behavior is a dynamic phenomenon unique to hybrid systems in which an infinite number of discrete transitions occurs in a finite amount of time. This behavior commonly arises in mechanical systems undergoing impacts and optimal control problems, but its characterization for general hybrid systems is not completely understood. The goal of this paper is to develop a stability theory for Zeno hybrid systems that parallels classical Lyapunov theory; that is, we present Lyapunov-like sufficient conditions for Zeno behavior obtained by mapping solutions of complex hybrid systems to solutions of simpler Zeno hybrid systems defined on the first quadrant of the plane. These conditions are applied to Lagrangian hybrid systems, which model mechanical systems undergoing impacts, yielding simple sufficient conditions for Zeno behavior. Finally, the results are applied to robotic bipedal walking. © 2012 IEEE.

Stabilization and disturbance attenuation of nonlinear systems using dissipativity theory

In this paper, we survey some recent results on stabilization and disturbance attenuation for nonlinear systems using a dissipativity approach. After reviewing the basic dissipativity concept, we stress the connections between Lyapunov designs and the problem of achieving passivity by feedback. Focusing on physical models, we then illustrate how the design of stabilizing feedback can take advantage of the natural energy balance equation of the system. Here stabilization is viewed as the task of shaping the energy of the system to enforce a minimum at the desired equilibrium. Finally, we show the implications of dissipativity theory as an appropriate framework to study the nonlinear H∞ control problem. © 2002 EUCA.