Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Suboptimal Markovian smoothing estimates based on continuous curves of solutions of the Algebraic Riccati Equation

Based on a result on continuous dependence of solutions of an algebraic Riccati equation on the data matrices, we construct continuous curves of solutions of an algebraic Riccati inequality, and derive suboptimal Markovian estimates for the steady-state smoothing problem

Modelling and Inverse Problems of Control for Distributed Parameter Systems; Proceedings of IFIP(W.G. 7.2)-IIASA Conference, July 24-28, 1989

The techniques of solving inverse problems that arise in the estimation and control of distributed parameter systems in the face of uncertainty as well as the applications of these to mathematical modelling for problems of applied system analysis (environmental issues, technological processes, biomathematical models, mathematical economy and other fields) are among the major topics of research at the Dynamic Systems Project of the Systems and Decision Sciences (SDS) Program at IIASA. In July 1989 the SDS Program was a coorganizer of a regular IFIP (WG 7.2) conference on Modelling and Inverse Problems of Control for Distributed Parameter Systems that was held at IIASA, and was attended by a number of prominent theorists and practitioners. One of the main purpose of this meeting was to review recent developments and perspectives in this field. The proceedings are presented in this volume

Active Information Acquisition With Mobile Robots

The recent proliferation of sensors and robots has potential to transform fields as diverse as environmental monitoring, security and surveillance, localization and mapping, and structure inspection. One of the great technical challenges in these scenarios is to control the sensors and robots in order to extract accurate information about various physical phenomena autonomously. The goal of this dissertation is to provide a unified approach for active information acquisition with a team of sensing robots. We formulate a decision problem for maximizing relevant information measures, constrained by the motion capabilities and sensing modalities of the robots, and focus on the design of a scalable control strategy for the robot team. The first part of the dissertation studies the active information acquisition problem in the special case of linear Gaussian sensing and mobility models. We show that the classical principle of separation between estimation and control holds in this case. It enables us to reduce the original stochastic optimal control problem to a deterministic version and to provide an optimal centralized solution. Unfortunately, the complexity of obtaining the optimal solution scales exponentially with the length of the planning horizon and the number of robots. We develop approximation algorithms to manage the complexity in both of these factors and provide theoretical performance guarantees. Applications in gas concentration mapping, joint localization and vehicle tracking in sensor networks, and active multi-robot localization and mapping are presented. Coupled with linearization and model predictive control, our algorithms can even generate adaptive control policies for nonlinear sensing and mobility models. Linear Gaussian information seeking, however, cannot be applied directly in the presence of sensing nuisances such as missed detections, false alarms, and ambiguous data association or when some sensor observations are discrete (e.g., object classes, medical alarms) or, even worse, when the sensing and target models are entirely unknown. The second part of the dissertation considers these complications in the context of two applications: active localization from semantic observations (e.g, recognized objects) and radio signal source seeking. The complexity of the target inference problem forces us to resort to greedy planning of the sensor trajectories. Non-greedy closed-loop information acquisition with general discrete models is achieved in the final part of the dissertation via dynamic programming and Monte Carlo tree search algorithms. Applications in active object recognition and pose estimation are presented. The techniques developed in this thesis offer an effective and scalable approach for controlled information acquisition with multiple sensing robots and have broad applications to environmental monitoring, search and rescue, security and surveillance, localization and mapping, precision agriculture, and structure inspection

Stochastic Event-Based Control and Estimation

Digital controllers are traditionally implemented using periodic sampling, computation, and actuation events. As more control systems are implemented to share limited network and CPU bandwidth with other tasks, it is becoming increasingly attractive to use some form of event-based control instead, where precious events are used only when needed. Forms of event-based control have been used in practice for a very long time, but mostly in an ad-hoc way. Though optimal solutions to most event-based control problems are unknown, it should still be viable to compare performance between suggested approaches in a reasonable manner. This thesis investigates an event-based variation on the stochastic linear-quadratic (LQ) control problem, with a fixed cost per control event. The sporadic constraint of an enforced minimum inter-event time is introduced, yielding a mixed continuous-/discrete-time formulation. The quantitative trade-off between event rate and control performance is compared between periodic and sporadic control. Example problems for first-order plants are investigated, for a single control loop and for multiple loops closed over a shared medium. Path constraints are introduced to model and analyze higher-order event-based control systems. This component-based approach to stochastic hybrid systems allows to express continuous- and discrete-time dynamics, state and switching constraints, control laws, and stochastic disturbances in the same model. Sum-of-squares techniques are then used to find bounds on control objectives using convex semidefinite programming. The thesis also considers state estimation for discrete time linear stochastic systems from measurements with convex set uncertainty. The Bayesian observer is considered given log-concave process disturbances and measurement likelihoods. Strong log-concavity is introduced, and it is shown that the observer preserves log-concavity, and propagates strong log-concavity like inverse covariance in a Kalman filter. A recursive state estimator is developed for systems with both stochastic and set-bounded process and measurement noise terms. A time-varying linear filter gain is optimized using convex semidefinite programming and ellipsoidal over-approximation, given a relative weight on the two kinds of error

Probabilistic Framework for Sensor Management

A probabilistic sensor management framework is introduced, which maximizes the utility of sensor systems with many different sensing modalities by dynamically configuring the sensor system in the most beneficial way. For this purpose, techniques from stochastic control and Bayesian estimation are combined such that long-term effects of possible sensor configurations and stochastic uncertainties resulting from noisy measurements can be incorporated into the sensor management decisions

Feynman-Kac Numerical Techniques for Stochastic Optimal Control

Three significant advancements are proposed for improving numerical methods in the solution of forward-backward stochastic differential equations (FBSDEs) appearing in the Feynman-Kac representation of the value function in stochastic optimal control (SOC) problems. First, we propose a novel characterization of FBSDE estimators as either on-policy or off-policy, highlighting the intuition for these techniques that the distribution over which value functions are approximated should, to some extent, match the distribution the policies generate. Second, two novel numerical estimators are proposed for improving the accuracy of single-timestep updates. In the case of LQR problems, we demonstrate both in theory and in numerical simulation that our estimators result in near machine-precision level accuracy, in contrast to previously proposed methods that can potentially diverge on the same problems. Third, we propose a new method for accelerating the global convergence of FBSDE methods. By the repeated use of the Girsanov change of probability measures, it is demonstrated how a McKean-Markov branched sampling method can be utilized for the forward integration pass, as long as the controlled drift terms are appropriately compensated in the backward integration pass. Subsequently, a numerical approximation of the value function is proposed by solving a series of function approximation problems backwards in time along the edges of a space-filling tree.Ph.D

Systems reliability issues for future aircraft

The reliability of adaptive controls for future aircraft are discussed. The research, formulation, and experimentation for improved aircraft performance are considered