Finite-time behavior of inner systems

In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller

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

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

Data-driven adaptive model-based predictive control with application in wastewater systems

This study is concerned with the development of a new data-driven adaptive model-based predictive controller (MBPC) with input constraints. The proposed methods employ subspace identification technique and a singular value decomposition (SVD)-based optimisation strategy to formulate the control algorithm and incorporate the input constraints. Both direct adaptive model-based predictive controller (DAMBPC) and indirect adaptive model-based predictive controller (IAMBPC) are considered. In DAMBPC, the direct identification of controller parameters is desired to reduce the design effort and computational load while the IAMBPC involves a two-stage process of model identification and controller design. The former method only requires a single QR decomposition for obtaining the controller parameters and uses a receding horizon approach to process input/output data for the identification. A suboptimal SVD-based optimisation technique is proposed to incorporate the input constraints. The proposed techniques are implemented and tested on a fourth order non-linear model of a wastewater system. Simulation results are presented to compare the direct and indirect adaptive methods and to demonstrate the performance of the proposed algorithms

Adaptive Optimal Control The Thinking Man's GPC

Exploring connections between adaptive control theory and practice, this book treats the techniques of linear quadratic optimal control and estimation (Kalman filtering), recursive identification, linear systems theory and robust arguments

Offset-free receding horizon control of constrained linear systems

The design of a dynamic state feedback receding horizon controller is addressed, which guarantees robust constraint satisfaction, robust stability and offset-firee control of constrained linear systems in the presence of time-varying setpoints and unmeasured disturbances. This objective is obtained by first designing a dynamic linear offset-free controller and computing an appropriate domain of attraction for this controller. The linear (unconstrained) controller is then modified by adding a perturbation term, which is computed by a (constrained) robust receding horizon controller. The receding horizon controller has the property that its domain of attraction contains that of the linear controller. In order to ensure robust constraint satisfaction, in addition to offset-free control, the transient, as well as the limiting behavior of the disturbance and setpoint need to be taken into account in the design of the receding horizon controller. The fundamental difference between the results and the existing literature on receding horizon control is that the transient effect of the disturbance and set point sequences on the so-called "target calculator" is explicitly incorporated in the formulation of the receding horizon controller. An example of the control of a continuous stirred-tank reactor is presented. (c) 2005 American Institute of Chemical Engineers

Optimal control approaches for persistent monitoring problems.

Thesis (Ph. D.)--Boston UniversityPersistent monitoring tasks arise when agents must monitor a dynamically changing environment which cannot be fully covered by a stationary team of available agents. It differs from traditional coverage tasks due to the perpetual need to cover a changing environment, i.e., all areas of the mission space must be visited infinitely often. This dissertation presents an optimal control framework for persistent monitoring problems where the objective is to control the movement of multiple cooperating agents to minimize an uncertainty metric in a given mission space. In an one-dimensional mission space, it is shown that the optimal solution is for each agent to move at maximal speed from one switching point to the next, possibly waiting some time at each point before reversing its direction. Thus, the solution is reduced to a simpler parametric optimization problem: determining a sequence of switching locations and associated waiting times at these switching points for each agent. This amounts to a hybrid system which is analyzed using Infinitesimal Perturbation Analysis (IPA) , to obtain a complete on-line solution through a gradient-based algorithm. IPA is a method used to provide unbiased gradient estimates of performance metrics with respect to various controllable parameters in Discrete Event Systems (DES) as well as in Hybrid Systems (HS). It is also shown that the solution is robust with respect to the uncertainty model used, i.e., IPA provides an unbiased estimate of the gradient without any detailed knowledge of how uncertainty affects the mission space. In a two-dimensional mission space, such simple solutions can no longer be derived. An alternative is to optimally assign each agent a linear trajectory, motivated by the one dimensional analysis. It is proved, however, that elliptical trajectories outperform linear ones. With this motivation, the dissertation formulates a parametric optimization problem to determine such trajectories. It is again shown that the problem can be solved using IPA to obtain performance gradients on line and obtain a complete and scalable solution. Since the solutions obtained are generally locally optimal, a stochastic comparison algorithm is incorporated for deriving globally optimal elliptical trajectories. The dissertation also approaches the problem by representing an agent trajectory in terms of general function families characterized by a set of parameters to be optimized. The approach is applied to the family of Lissajous functions as well as a Fourier series representation of an agent trajectory. Numerical examples indicate that this scalable approach provides solutions that are near optimal relative to those obtained through a computationally intensive two point boundary value problem (TPBVP) solver. In the end, the problem is tackled using centralized and decentralized Receding Horizon Control (RHC) algorithms, which dynamically determine the control for agents by solving a sequence of optimization problems over a planning horizon and executing them over a shorter action horizon