http://control.disp.uniroma2.it/galeani/CO/materiale/automatica2000.pdf

Survey Constrained model predictive control: Stability and optimality

We address the controller design and the trajectory generation for a quadrotor maneuvering in three dimensions in a tightly constrained setting typical of indoor environments. In such settings, it is necessary to allow for significant excursions of the attitude from the hover state and small angle approximations cannot be justified for the roll and pitch. We develop an algorithm that enables the real-time generation of optimal trajectories through a sequence of 3-D positions and yaw angles, while ensuring safe passage through specified corridors and satisfying constraints on velocities, accelerations and inputs. A nonlinear controller ensures the faithful tracking of these trajectories. Experimental results illustrate the application of the method to fast motion (5–10 body lengths/second) in three-dimensional slalom courses.

Minimum snap trajectory generation and control for quadrotors

Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.

Predictive Control for Linear and Hybrid Systems

We study the problem of designing dynamically feasible trajectories and controllers that drive a quadrotor to a desired state in state space. We focus on the development of a family of trajectories defined as a sequence of segments, each with a controller parameterized by a goal state or region in state space. Each controller is developed from the dynamic model of the robot and then iteratively refined through successive experimental trials in an automated fashion to account for errors in the dynamic model and noise in the actuators and sensors. We show that this approach permits the development of trajectories and controllers enabling such aggressive maneuvers as flying through narrow, vertical gaps and perching on inverted surfaces with high precision and repeatability.

Trajectory generation and control for precise aggressive maneuvers with quadrotors

Multiparametric Programming- Multiparametric Programming: a Geometric Approach- Optimal Control of Linear Systems- Constrained Finite Time Optimal Control- Constrained Infinite Time Optimal Control- Receding Horizon Control- Constrained Robust Optimal Control- Reducing On-line Complexity- Optimal Control of Hybrid Systems- Hybrid Systems- Constrained Optimal Control for Hybrid Systems- Applications- Ball and Plate- Traction Control

Constrained Optimal Control of Linear and Hybrid Systems

It is well known that unconstrained infinite-horizon optimal control may be used to construct a stabilizing controller for a nonlinear system. We show that similar stabilization results may be achieved using unconstrained finite horizon optimal control. The key idea is to approximate the tail of the infinite horizon cost-to-go using, as terminal cost, an appropriate control Lyapunov function. Roughly speaking, the terminal control Lyapunov function (CLF) should provide an (incremental) upper bound on the cost. In this fashion, important stability characteristics may be retained without the use of terminal constraints such as those employed by a number of other researchers. The absence of constraints allows a significant speedup in computation. Furthermore, it is shown that in order to guarantee stability, it suffices to satisfy an improvement property, thereby relaxing the requirement that truly optimal trajectories be found. We provide a complete analysis of the stability and region of attraction/operation properties of receding horizon control strategies that utilize finite horizon approximations in the proposed class. It is shown that the guaranteed region of operation contains that of the CLF controller and may be made as large as desired by increasing the optimization horizon (restricted, of course, to the infinite horizon domain). Moreover, it is easily seen that both CLF and infinite-horizon optimal control approaches are limiting cases of our receding horizon strategy. The key results are illustrated using a familiar example, the inverted pendulum, where significant improvements in guaranteed region of operation and cost are noted.

/pdf/unconstrained-receding-horizon-control-of-nonlinear-systems-tbzkhia9vk.pdf

Unconstrained receding-horizon control of nonlinear systems

A modified version of the receding horizon control of nonlinear systems is proposed. The approach is based on a finite horizon optimal control problem with a terminal cost. This method can be treated as an extension of results of De Nicolao et al. (1998). To the case where a control Lyapunov function (CLF)-based stabilizing control law is available. The terminal cost is picked to be a CLF which is also an upper bound on the cost-to-go if the stabilizing control law is applied. The control law is computed a priori using a CLF. Effectiveness of the results is illustrated by applying this approach to the planar model of a ducted fan with a CLF obtained using quasi LPV methods.

Stabilizing receding horizon control of nonlinear systems: a control Lyapunov function approach

Brief Comparison of nonlinear control design techniques on a model of the Caltech ducted fan

Deals with the application of receding horizon methods to the simplified model of a flight control experiment developed at Cal Tech. The dynamics of the system are representative of a vertical take off and landing (VTOL) aircraft, such as a Harrier around hover. The adopted control methodology is a hybrid of receding horizon techniques and control Lyapunov function (CLF) based ideas. First a CLF is found, and then, by using the CLF as the terminal cost in the receding horizon optimization, stability is guaranteed. It is shown that if the horizon length is long enough, a simple choice of CLF, i.e., the one obtained from Jacobian linearization of the dynamics at hover, will achieve a good performance. However, if due to computational costs, longer time horizons are not possible, stability can be guaranteed by applying the CLF obtained using quasi-LPV methods, as a terminal cost. Several numerical simulations for different time horizons are presented to illustrate the effectiveness of the discussed methods.

Receding horizon control of the Caltech ducted fan: a control Lyapunov function approach

It is well known that unconstrained infinite horizon optimal control may be used to construct a stabilizing controller for a nonlinear system. In this paper, we show that similar stabilization results may be achieved using unconstrained finite horizon optimal control. The key idea is to approximate the tail of the infinite horizon cost-to-go using, as terminal cost, an appropriate control Lyapunov function (CLF). We provide a complete analysis of the stability and region of attraction/operation properties of receding horizon control strategies that utilize finite horizon approximations in the proposed class. It is shown that the guaranteed region of operation contains that of the CLF controller and may be made as large as desired by increasing the optimization horizon (restricted, of course, to the infinite horizon domain). The key results are illustrated using a familiar example, the inverted pendulum, where significant improvements in guaranteed region of operation and cost are noted.

/pdf/unconstrained-receding-horizon-control-of-nonlinear-systems-42hct18b1o.pdf

Jie Yu

Papers

Unconstrained receding-horizon control of nonlinear systems

Stabilizing receding horizon control of nonlinear systems: a control Lyapunov function approach

Brief Comparison of nonlinear control design techniques on a model of the Caltech ducted fan

Receding horizon control of the Caltech ducted fan: a control Lyapunov function approach

Unconstrained receding horizon control of nonlinear systems