A stable model predictive control algorithm without terminal weighting

The introduction of terminal penalty in the performance index and the usage of the concept of terminal regions now become common practice in Model Predictive Control (MPC) for guaranteeing its stability. However, it is quite difficult and conservative to propagate the influence of disturbances and uncertainties from an initial state to the terminal state, in particular, when the predictive horizon is long. This paper presents a new stable MPC algorithm where the additional weighting on the first state rather than on the terminal state in the horizon is imposed. Furthermore, a new tuning knob is introduced in the performance index, which can be used to trade off between disturbance attenuation/robustness and stability. It is shown that in the absence of disturbances and uncertainties, the new MPC algorithm achieves the similar performance as current terminal weighting based MPC algorithms. However, it exhibits much better disturbance attenuation ability and robustness against uncertainties. The proposed method is favorably compared with terminal weighting based MPC algorithms by a numerical example

Model predictive control of low Earth-orbiting satellites using magnetic actuation

This paper presents a model predictive control approach for regulating the attitude of magnetically actuated satellites. Unlike other contributions in this area, a predictive control approach is developed which guarantees closed-loop stability of satellite configurations with unstable open-loop pitch dynamics. With the pitch axis being unstable, two magnetic dipoles are used exclusively for regulation of this axis. This allows the dynamics to be treated as a linear time-invariant system, and a simple proportional–derivative (PD) scheme is implemented. A model predictive controller is designed to regulate the lateral dynamics, with a Lyapunov function derived to guarantee asymptotic stability of the closed-loop system. The regulation of the lateral dynamics is achieved with a singe dipole moment, with a novel reformulation of the lateral dynamics also providing an explicit link between the two controllers. Simulations demonstrate the effectiveness and stability of the proposed algorithm when applied to the European Space Agency’s GOCE satellite

Robust model predictive control for normbounded uncertain systems using new parameter dependent terminal weighting matrix,

Abstract A new robust model predictive control (MPC) technique is proposed for norm-bounded uncertain systems with input constraints. In order to improve feasibility and system performance, we propose an LMI condition for the cost monotonicity by using a new parameter dependent terminal weighting matrix. We formulate the problem as a minimization of the upper bound of infinite horizon cost function subject to the LMI condition for the cost monotonicity. A numerical example shows the effectiveness of the proposed method

Design of Stabilizing Receding Horizon Controls for Constrained Linear Time-Varying Systems

In this paper, we propose a generalized stabilizing receding horizon control (RHC) scheme for input/state constrained linear discrete time-varying systems that improves feasibility and on-line computation on the constrained finite-horizon optimization problem, compared with existing schemes. The control scheme is based on a time-varying horizon cost function with time-varying terminal weighting matrices, which can easily be implemented via linear matrix inequality (LMI) optimization. We discuss modifications of the proposed scheme that improve feasibility or on-line computation time. Through various simulation examples, we illustrate the results of these schemes

Autonomous Control of Space Reactor Systems

Autonomous and semi-autonomous control is a key element of space reactor design in order to meet the mission requirements of safety, reliability, survivability, and life expectancy. Interrestrial nuclear power plants, human operators are avilable to perform intelligent control functions that are necessary for both normal and abnormal operational conditions

Control de un robot autónomo móvil para la recogida de objetos (mejora del rendimiento en el control de manipuladores robóticos mediante combinación de técnicas de control robusto y predictivo)

Classical control techniques for robot manipulators do not deal effectively with problems such as model uncertainties, completely unknown disturbances and constraints. In this thesis some robust and control techniques are designed and implemented with better performance in terms of robustness and computational efficiency with respect to the classical techniques. Real results obtained from an industrial manipulator show the efficiency and improvement of these new techniques with respect to up-to-day proposed ones.Las técnicas clásicas de control de manipuladores robóticos no tratan eficientemente problemas tales como las incertidumbres del modelo, perturbaciones totalmente desconocidas y ligaduras. En esta tesis se diseñan e implementan técnicas de control robusto y predictivo que añaden mejores prestaciones en términos de robustez y eficiencia computacional respecto a las técnicas clásicas. Los resultados reales obtenidos con un manipulador industrial muestran la eficiencia y la mejora de estas nuevas técnicas respecto a las presentes en la literatura actual

Stability Of Receding Horizon Control Of Nonlinear Systems

This paper focus on the stability of receding horizon control of general nonlinear systems. We employ a recent result on the convergence of the cost functional and we show that the cost induces a Lyapunov function along the receding horizon trajectories. The result requires a notion of detectability of nonlinear systems and a condition on the horizon length. Contrary to the usual approaches, we do not impose end-point constraints or special terminal weighting. In the particular linear setting, we show that the requirements imposed in the general case are reduced to the standard detectability and stabilizability conditions.320772081Anderson, B.D.O., Moore, J.B., Detectability and stabilizability of time-varying discrete-time linear Systems (1981) SIAM Journal on Control and Optimization, 19 (1), pp. 20-32Chen, C., Shaw, L., On receding horizon feedback control (1982) Automatica, pp. 349-352Costa, E.F., Do Val, J.B.R., Optimal cost convergence with respect to the time horizon (2003) European Control Conference, , Cambridge, UK (Submitted)De Nicolao, G., Strada, S., On the stability of receding-horizon LQ Control with zero-state terminal contraint (1997) IEEE Transactions on Automatic Control, 42 (2), pp. 257-260Hager, W.W., Horowitz, L.L., Convergence and stability properties of the discrete Riccati operator equation and the associated optimal control and filtering problems (1976) SIAM Journal on Control and Optimization, 14 (2), pp. 295-312Kailath, T., (1980) Linear Systems, , Prentice-HallKeerthi, S.S., Gilbert, E.G., Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations (1988) Journal of Optimization Theory and Applications, 57 (2), pp. 265-293Kothare, M.V., Balakrishnan, V., Morari, M., Robust constrained model predictive control using linear matrix inequalities (1996) Automatica, 32 (10), pp. 1361-1379Kwon, W.H., Pearson, A.E., A modified quadratic cost problem and feedback stabilization of a linear system (1977) IEEE Transactions on Automatic Control, 22 (5), pp. 838-842Lee, J.W., Kwon, W.H., Choi, J., On stability of constrained receding horizon control with finite terminal weighting matrix (1998) Automatica, 34 (12), pp. 1607-1612Lee, Y.I., Kouvaritakis, B., Constrained receding horizon predictive control for systems with disturbances (1999) International Journal of Control, 72 (11), pp. 1027-1032Mayne, D.Q., Michalska, H., Receeding horizon control of nonlinear systems (1990) IEEE Transactions on Automatic Control, 35, pp. 814-824Mosca, E., Zhang, J., Stable redesign of predictive control (1992) Automatica, 28 (6), pp. 1229-1233Primbs, J.A., Nevistic, V., A new approach to stability analysis for constrained finite receding horizon control without end constraints (2000) IEEE Transactions on Automatic Control, 45, pp. 1507-1512Rawlings, J.B., Muske, K.R., The stability of constrained receding horizon control (1993) IEEE Transactions on Automatic Control, 38 (10), pp. 1512-151

Obtaining Stabilizing Stationary Controls Via Finite Horizon Cost

This paper focus on the stabilizing properties of stationary feedback controls for general nonlinear systems that are obtained by minimizing a finite horizon cost, in a receding horizon control basis. The main result is to establish exponential stability for stationary controls obtained from minimization of sufficiently large but finite time horizon cost. The approach requires a previously defined notion of closed-loop detectability of nonlinear systems, and in the present paper we introduce conditions under which the aforementioned detectability sense is verified from the open-loop system data, as is usual in linear systems. In connection, we verify that stabilizable and detectable linear time-invariant systems satisfy each of the work assumptions. © 2006 IEEE.200642974302Anderson, B.D.O., Moore, J.B., Detectability and stabilizability of time-varying discrete-time linear systems (1981) SIAM Journal on Control and Optimization, 19 (1), pp. 20-32Costa, E.F., do Val, J.B.R., Optimal cost convergence with respect to the time horizon (2003) ECC'03 European Control Conference, pp. 1-6. , Cambridge, United KingdomCosta, E.F., do Val, J.B.R., Stability of receding horizon control of nonlinear systems (2003) 42st IEEE Conference on Decision and Control, pp. 2077-2081. , Maui, Hawaii, USA, IEEECosta, E.F., do Val, J.B.R., A finite-time stability concept and conditions for finite-time and exponential stability of controlled nonlinear systems (2006) Submitted to the ACC'06 American Control ConferenceDe Nicolao, G., Strada, S., On the stability of receding-horizon LQ Control with zero-state terminal contraint (1997) IEEE Transactions on Automatic Control, 42 (2), pp. 257-260Hager, W.W., Horowitz, L.L., Convergence and stability properties of the discrete Riccati operator equation and the associated optimal control and filtering problems (1976) SIAM Journal on Control and Optimization, 14 (2), pp. 295-312Ito, K., Kunisch, K., Asymptotic properties of receding horizon optimal control problems (2002) Siam Journal on Control and Optimization, 40 (5), pp. 1585-1610Jadbabaie, A., Hauser, J., On the stablity of unconstrained receding horizon control with a general terminal cost (2001) Conference on Decicion and Control 2001Kailath, T., (1980) Linear Systems, , Prentice-HallKothare, M.V., Balakrishnan, V., Morari, M., Robust constrained model predictive control using linear matrix inequalities (1996) Automatica, 32 (10), pp. 1361-1379Lee, J.W., Kwon, W.H., Choi, J., On stability of constrained receding horizon control with finite terminal weighting matrix (1998) Automatica, 34 (12), pp. 1607-1612Lee, Y.I., Kouvaritakis, B., Constrained receding horizon predictive control for systems with disturbances (1999) International Journal of Control, 72 (11), pp. 1027-1032Mayne, D.Q., Michalska, H., Receeding horizon control of nonlinear systems (1990) IEEE Transactions on Automatic Control, 35, pp. 814-824Mosca, E., Zhang, J., Stable redesign of predictive control (1992) Automatica, 28 (6), pp. 1229-1233Primbs, J.A., Nevistic, V., A new approach to stability analysis for constrained finite receding horizon control without end constraints (2000) IEEE Transactions on Automatic Control, 45, pp. 1507-1512Rawlings, J.B., Muske, K.R., The stability of constrained receding horizon control (1993) IEEE Transactions on Automatic Control, 38 (10), pp. 1512-151