3,595 research outputs found
Stochastic model predictive control of LPV systems via scenario optimization
A stochastic receding-horizon control approach for constrained Linear Parameter Varying discrete-time systems is proposed in this paper. It is assumed that the time-varying parameters have stochastic nature and that the system's matrices are bounded but otherwise arbitrary nonlinear functions of these parameters. No specific assumption on the statistics of the parameters is required. By using a randomization approach, a scenario-based finite-horizon optimal control problem is formulated, where only a finite number M of sampled predicted parameter trajectories (‘scenarios') are considered. This problem is convex and its solution is a priori guaranteed to be probabilistically robust, up to a user-defined probability level p. The p level is linked to M by an analytic relationship, which establishes a tradeoff between computational complexity and robustness of the solution. Then, a receding horizon strategy is presented, involving the iterated solution of a scenario-based finite-horizon control problem at each time step. Our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time, either deterministically, or with probability no smaller than p. The features of the approach are illustrated by a numerical example
Robust Temporal Logic Model Predictive Control
Control synthesis from temporal logic specifications has gained popularity in
recent years. In this paper, we use a model predictive approach to control
discrete time linear systems with additive bounded disturbances subject to
constraints given as formulas of signal temporal logic (STL). We introduce a
(conservative) computationally efficient framework to synthesize control
strategies based on mixed integer programs. The designed controllers satisfy
the temporal logic requirements, are robust to all possible realizations of the
disturbances, and optimal with respect to a cost function. In case the temporal
logic constraint is infeasible, the controller satisfies a relaxed, minimally
violating constraint. An illustrative case study is included.Comment: This work has been accepted to appear in the proceedings of 53rd
Annual Allerton Conference on Communication, Control and Computing,
Urbana-Champaign, IL (2015
On output feedback nonlinear model predictive control using high gain observers for a class of systems
In recent years, nonlinear model predictive control schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in connection to nonlinear predictive control. Most of the existing approaches for output feedback nonlinear model predictive control do only guarantee local stability. Here we consider the combination of stabilizing instantaneous NMPC schemes with high gain observers. For a special MIMO system class we show that the closed loop is asymptotically stable, and that the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme are recovered for a high gain observer with large enough gain and thus leading to semi-global/non-local results
Robust Constrained Model Predictive Control using Linear Matrix Inequalities
The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a state-feedback control law which minimizes a "worst-case" infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques, the problem of minimizing an upper bound on the "worst-case" objective function, subject to input and output constraints, is reduced to a convex optimization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon state-feedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions, such as application to systems with time-delays and problems involving constant set-point tracking, trajectory tracking and disturbance rejection, which follow naturally from our formulation, are discussed. The controller design procedure is illustrated with two examples. Finally, conclusions are presented
Reducing the Prediction Horizon in NMPC: An Algorithm Based Approach
In order to guarantee stability, known results for MPC without additional
terminal costs or endpoint constraints often require rather large prediction
horizons. Still, stable behavior of closed loop solutions can often be observed
even for shorter horizons. Here, we make use of the recent observation that
stability can be guaranteed for smaller prediction horizons via Lyapunov
arguments if more than only the first control is implemented. Since such a
procedure may be harmful in terms of robustness, we derive conditions which
allow to increase the rate at which state measurements are used for feedback
while maintaining stability and desired performance specifications. Our main
contribution consists in developing two algorithms based on the deduced
conditions and a corresponding stability theorem which ensures asymptotic
stability for the MPC closed loop for significantly shorter prediction
horizons.Comment: 6 pages, 3 figure
Optimal Switching Synthesis for Jump Linear Systems with Gaussian initial state uncertainty
This paper provides a method to design an optimal switching sequence for jump
linear systems with given Gaussian initial state uncertainty. In the practical
perspective, the initial state contains some uncertainties that come from
measurement errors or sensor inaccuracies and we assume that the type of this
uncertainty has the form of Gaussian distribution. In order to cope with
Gaussian initial state uncertainty and to measure the system performance,
Wasserstein metric that defines the distance between probability density
functions is used. Combining with the receding horizon framework, an optimal
switching sequence for jump linear systems can be obtained by minimizing the
objective function that is expressed in terms of Wasserstein distance. The
proposed optimal switching synthesis also guarantees the mean square stability
for jump linear systems. The validations of the proposed methods are verified
by examples.Comment: ASME Dynamic Systems and Control Conference (DSCC), 201
Nonlinear Receding-Horizon Control of Rigid Link Robot Manipulators
The approximate nonlinear receding-horizon control law is used to treat the
trajectory tracking control problem of rigid link robot manipulators. The
derived nonlinear predictive law uses a quadratic performance index of the
predicted tracking error and the predicted control effort. A key feature of
this control law is that, for their implementation, there is no need to perform
an online optimization, and asymptotic tracking of smooth reference
trajectories is guaranteed. It is shown that this controller achieves the
positions tracking objectives via link position measurements. The stability
convergence of the output tracking error to the origin is proved. To enhance
the robustness of the closed loop system with respect to payload uncertainties
and viscous friction, an integral action is introduced in the loop. A nonlinear
observer is used to estimate velocity. Simulation results for a two-link rigid
robot are performed to validate the performance of the proposed controller.
Keywords: receding-horizon control, nonlinear observer, robot manipulators,
integral action, robustness
Model Predictive Control: Multivariable Control Technique of Choice in the 1990s?
The state space and input/output formulations of model predictive control are compared and preference is given to the former because of the industrial interest in multivariable constrained problems. Recently, by abandoning the assumption of a finite output horizon several researchers have derived powerful stability results for linear and nonlinear systems with and without constraints, for the nominal case and in the presence of model uncertainty. Some of these results are reviewed. Optimistic speculations about the future of MPC conclude the paper
- …