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 nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

Model Predictive Control of stochastic LPV Systems via Random Convex Programs

This paper considers the problem of stabilization of stochastic Linear Parameter Varying (LPV) discrete time systems in the presence of convex state and input constraints. By using a randomization approach, a convex finite horizon optimal control problem is derived, even when the dependence of the system's matrices on the time-varying parameters is nonlinear. This convex problem can be solved efficiently, and its solution is a-priori guaranteed to be probabilistically robust, up to a user-defined probability level p. Then, a novel receding horizon control strategy that involves, at each time step, the solution of a finite-horizon scenario-based control problem, is proposed. It is shown that the resulting closed loop scheme drives the state to a terminal set in finite time, either deterministically, or with probability no less than p. The features of the approach are shown through a numerical exampl

Optimal control and robust estimation for ocean wave energy converters

This thesis deals with the optimal control of wave energy converters and some associated observer design problems. The first part of the thesis will investigate model predictive control of an ocean wave energy converter to maximize extracted power. A generic heaving converter that can have both linear dampers and active elements as a power take-off system is considered and an efficient optimal control algorithm is developed for use within a receding horizon control framework. The optimal control is also characterized analytically. A direct transcription of the optimal control problem is also considered as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard nonlinear program solver. Since the system model is bilinear and the cost function is not convex quadratic, the resulting optimization problem is shown not to be a quadratic program. Results are compared with other methods like optimal latching to demonstrate the improvement in absorbed power under irregular sea condition simulations. In the second part, robust estimation of the radiation forces and states inherent in the optimal control of wave energy converters is considered. Motivated by this, low order H∞ observer design for bilinear systems with input constraints is investigated and numerically tractable methods for design are developed. A bilinear Luenberger type observer is formulated and the resulting synthesis problem reformulated as that for a linear parameter varying system. A bilinear matrix inequality problem is then solved to find nominal and robust quadratically stable observers. The performance of these observers is compared with that of an extended Kalman filter. The robustness of the observers to parameter uncertainty and to variation in the radiation subsystem model order is also investigated. This thesis also explores the numerical integration of bilinear control systems with zero-order hold on the control inputs. Making use of exponential integrators, exact to high accuracy integration is proposed for such systems. New a priori bounds are derived on the computational complexity of integrating bilinear systems with a given error tolerance. Employing our new bounds on computational complexity, we propose a direct exponential integrator to solve bilinear ODEs via the solution of sparse linear systems of equations. Based on this, a novel sparse direct collocation of bilinear systems for optimal control is proposed. These integration schemes are also used within the indirect optimal control method discussed in the first part.Open Acces

Direct data-driven control of constrained linear parameter-varying systems: A hierarchical approach

In many nonlinear control problems, the plant can be accurately described by a linear model whose operating point depends on some measurable variables, called scheduling signals. When such a linear parameter-varying (LPV) model of the open-loop plant needs to be derived from a set of data, several issues arise in terms of parameterization, estimation, and validation of the model before designing the controller. Moreover, the way modeling errors affect the closed-loop performance is still largely unknown in the LPV context. In this paper, a direct data-driven control method is proposed to design LPV controllers directly from data without deriving a model of the plant. The main idea of the approach is to use a hierarchical control architecture, where the inner controller is designed to match a simple and a-priori specified closed-loop behavior. Then, an outer model predictive controller is synthesized to handle input/output constraints and to enhance the performance of the inner loop. The effectiveness of the approach is illustrated by means of a simulation and an experimental example. Practical implementation issues are also discussed.Comment: Preliminary version of the paper "Direct data-driven control of constrained systems" published in the IEEE Transactions on Control Systems Technolog

Modeling and Estimation of Biological Plants

Estimating the state of a dynamic system is an essential task for achieving important objectives such as process monitoring, identification, and control. Unlike linear systems, no systematic method exists for the design of observers for nonlinear systems. Although many researchers have devoted their attention to these issues for more than 30 years, there are still many open questions. We envisage that estimation plays a crucial role in biology because of the possibility of creating new avenues for biological studies and for the development of diagnostic, management, and treatment tools. To this end, this thesis aims to address two types of nonlinear estimation techniques, namely, the high-gain observer and the moving-horizon estimator with application to three different biological plants. After recalling basic definitions of stability and observability of dynamical systems and giving a bird's-eye survey of the available state estimation techniques, we are interested in the high-gain observers. These observers may be used when the system dynamics can be expressed in specific a coordinate under the so-called observability canonical form with the possibility to assign the rate of convergence arbitrarily by acting on a single parameter called the high-gain parameter. Despite the evident benefits of this class of observers, their use in real applications is questionable due to some drawbacks: numerical problems, the peaking phenomenon, and high sensitivity to measurement noise. The first part of the thesis aims to enrich the theory of high-gain observers with novel techniques to overcome or attenuate these challenging performance issues that arise when implementing such observers. The validity and applicability of our proposed techniques have been shown firstly on a simple one-gene regulatory network, and secondly on an SI epidemic model. The second part of the thesis studies the problem of state estimation using the moving horizon approach. The main advantage of MHE is that information about the system can be explicitly considered in the form of constraints and hence improve the estimates. In this work, we focus on estimation for nonlinear plants that can be rewritten in the form of quasi-linear parameter-varying systems with bounded unknown parameters. Moving-horizon estimators are proposed to estimate the state of such systems according to two different formulations, i.e., "optimistic" and "pessimistic". In the former case, we perform estimation by minimizing the least-squares moving-horizon cost with respect to both state variables and parameters simultaneously. In the latter, we minimize such a cost with respect to the state variables after picking up the maximum of the parameters. Under suitable assumptions, the stability of the estimation error given by the exponential boundedness is proved in both scenarios. Finally, the validity of our obtained results has been demonstrated through three different examples from biological and biomedical fields, namely, an example of one gene regulatory network, a two-stage SI epidemic model, and Amnioserosa cell's mechanical behavior during Dorsal closure

Control Allocation of Flexible Aircraft for Load Alleviation

As wing designs aim for higher aerodynamic efficiency, the underlying aircraft structure becomes more flexible, requiring additional features to alleviate the loads encountered from gusts and maneuvers. While alleviating loads, it is desirable to minimize the deviations from the original flight trajectory. In this work, a dynamic control allocation method which exploits redundant control effectors for maneuver and gust load alleviation is proposed for flexible aircraft. The control architecture decouples the two objectives of load alleviation and rigid body trajectory tracking by exploiting the null space between the input and the rigid body output. A reduced-dimensional null space input is established, which affects the flexible output (but not the rigid body output) when passed through a null space filter to generate incremental control signals. This null space input is determined to maintain the flexible output of the aircraft within specified values, thereby achieving load alleviation. A receding horizon approach to generate the trajectory of the null space input is developed based on linear aircraft models. This receding horizon approach then informs a model predictive control-based control allocator function which can be used as an add-on scheme to a nominal controller. Numerical simulations are used to illustrate the operation of this load alleviation system based on linear models, linear parameter-varying models, and nonlinear models. It is shown that the proposed load alleviation system can successfully avoid the violation of load bounds in the presence of both gust disturbances and maneuvers and with minimal effect on the trajectory tracking performance. A case study to characterize the proposed load alleviation system identified limits of its applicability to nonlinear aircraft and resulted in recommendations for its design parameters. The load alleviation system developed and demonstrated in this work can be applied to aircraft with wing flexibility high enough that the vertical wingtip deflection is around 28-34% of half-span in cruise and the first out-of-plane bending frequency is around 1.05-1.15 Hz. The case study also showed that a preview horizon of 1-2 seconds provides a good compromise for handling both low-frequency maneuvers and high-frequency gust disturbances.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168029/1/hansenjh_1.pd

Receding horizon control of vectored thrust flight experiment

Abstract: The application of a constrained receding horizon control technique to stabilise an indoor vectored-thrust flight experiment, known as the Caltech ducted fan, is given. The receding horizon control problem is formulated as a constrained optimal control problem and solved in real time with an efficient, computational method that combines nonlinear control theory, B-spline basis functions, and nonlinear programming. Characteristic issues, including non-zero computational times, convergence properties, choice of horizon length and terminal cost are discussed. The study validates the applicability of real-time receding horizon control for constrained systems with fast dynamics