Control Strategies for Players with Discrete and Uncertain Observations

In this paper we provide a design methodology to compute control strategies for a primary dynamical system which is operating in a domain where other dynamical systems are present and the interactions between these systems and the primary one are of interest or are being pursued in some sense. The information from the other systems is available to the primary dynamical system only at discrete time instances and is assumed to be corrupted by noise. Having available only this limited and somewhat corrupted information which depends on the noise, the primary system has to make a decision based on the estimated behavior of other systems which may range from cooperative to noncooperative. This decision is reflected in a design of the most appropriate action, that is, control strategy of the primary system. The design is illustrated by considering some particular collision avoidance problem scenarios.

In sensor networks, sensor measurements may be uncertain due to the impact of environment and different performances of sensors. In this paper, the cross-covariance matrix of prediction errors between any two sensor subsystems is derived for stochastic discrete-time linear systems with uncertain observations by using projection theory. Based on the linear minimum variance weighted fusion algorithm, the distributed information fusion Kalman predictor is obtained for stochastic systems with uncertain observations. It avoids the high-dimensional computation resorting to state augmentation, and has the better reliability. The simulation example verifies the effectiveness of the algorithm.

In this paper, the least-squares estimation problem of signals from uncertain observations coming from multiple sensors is addressed. Assuming that the probability distribution of the Bernoulli random variables modeling the uncertainty is not necessarily the same for all the sensors, recursive filtering and smoothing (fixed-point and fixed-interval) algorithms are proposed. The derivation of such algorithms does not require the knowledge of the signal state-space model, but only the covariance functions of the processes involved in the observation equations and the uncertainty probabilities. The application of the proposed algorithms is illustrated by a numerical simulation example wherein a signal is estimated from uncertain observations coming from two sensors with different uncertainty characteristics.

Interval Estimation for Linear Switched System

Considering discrete-time systems with uncertain observations when the signal model is unknown, but only covariance information is available, and the signal and the observation additive noise are correlated and jointly Gaussian, we present recursive algorithms for suboptimal fixed-point and fixed-interval smoothing estimators. To derive the algorithms, we employ a technique consisting in approximating the conditional distributions of the signal given the observations by Gaussian distributions, taking successive approximations of the mixtures of normal distributions. The expectation of these approximations provides us with the suboptimal estimators. In a numerical simulation example, the performance of the proposed estimators is compared with that of linear ones, via the sample mean square values of the corresponding estimation errors.

For linear discrete-time stochastic systems measured by multiple sensors, where different sensors are subject to mixed uncertainties of random delays, packet dropouts and/or uncertain observations, the centralized fusion linear optimal estimators in the linear minimum variance sense are presented via the innovation analysis approach, which is a general and useful tool to find the optimal linear estimate. The stability of the proposed estimators is analyzed. A sufficient condition for the existence of the centralized fusion steady-state estimators is given. For a single sensor case, the proposed estimators have the simpler forms and the lower computational cost compared to the existing literature, since a lower dimension parameterized system is constructed and the colored noise is avoided. A simulation example verifies the effectiveness of the proposed estimators.

This paper studies the problem of optimal filtering of discrete-time systems with random sensor delay, multiple packet dropout and uncertain observation. The random sensor delay, multiple packet dropout or uncertainty in observation is transformed to a stochastic parameter in the system representation. A new formulation enables us to design an optimal filter for a system with multiple packet dropout in sensor data. Based on a stochastic definition of the -norm of a system with a stochastic parameter, new relations for stochastic -norm are derived. The stochastic -norm of the estimation error is used as a criterion for the filter design. The relations derived for the new norm definition are used to obtain a set of linear matrix inequalities (LMIs) to solve the filter design problems. Simulation examples show the effectiveness of the proposed method.

Linear and quadratic estimation using uncertain observations from multiple sensors with correlated uncertainty

Different approaches for state filtering in nonlinear systems with uncertain observations

This paper is concerned with the covariance intersection (CI) fusion filtering problem for networked systems with multiple sensors subject to uncertain observations, random delays and losses of transmitted packets. Several groups of Bernoulli distributed random variables are used to depict the phenomena of uncertain observations, different random delays and losses of transmitted packets from different sensors to the fusion center. Using the innovation analysis approach, local optimal linear filter based on each sensor is presented in the linear minimum variance sense. Further, a distributed suboptimal fusion filter is obtained by using the CI fusion algorithm. It has the reduced computational burden since the computation of cross-covariance matrices is avoided. Moreover, it has better accuracy than any local filters. A simulation example verifies the effectiveness.

Stochastic partial differential equations (SPDE) are used for stochastic modelling, for instance, in the study of neuronal behaviour in neurophysiology and in building stochastic models for turbulence. Huebner, Khasminskii and Rozovskii (1993) started the investigation of the maximum likelihood estimation of the parameters involved in two types of SPDE's and extended their results for a class of parabolic SPDE's in Huebner and Rozovskii (1995). Prakasa Rao (1998,2000) obtained Bernstein - von Mises type theorems for a class of parabolic SPDE's and investigated the properties of Bayes estimators of parameters involved in such SPDE's. In all the papers cited earlier, it was assumed that a continuous observation of a random field uε( x, t) satisfying the SPDE over the region [0, 1] × [0, T] is available. It is obvious that this assumption is not tenable in practice and the problem of interest is to develop methods of estimation of parameters from the random field uε( x, t) observed at discrete times t and at discrete positions x or from the Fourier coefficients uiε( t) observed at discrete time instants. We construct consistent and asymptotically normal estimators of the parameter based on the Fourier coefficients uiε( t) observed at discrete times [Formula: see text] tends to infinity. AMS (2000) Subject classification: Primary 62 M 40; Secondary 60 H 15.

The study considers the problem of optimal control for linear discrete systems with a free right end of the trajectory and constraints on control. A new approach to constructing a discrete system is proposed and control is determined at discrete instants of time. Necessary and sufficient conditions for optimality are obtained and a method is proposed for the exact solution of the boundary value problem, which is reduced to solving a finite number of systems of algebraic equations. The proposed method for solving the optimal control problem for a discrete system allows to represent the desired optimal control in the form of synthesising control. For this, a positively definite symmetric matrix is defined that satisfies a difference equation of Riccati type. An algorithm for constructing control for discrete systems is developed, based on the feedback principle, taking into account constraints on the values of controls. The problem is solved using the Lagrange multipliers of a special form, which depend on the phase coordinates at discrete instants of time. The proposed method for solving the problem of optimal control with constraints on control values is implemented on a computer with an application package and tested for the task of planning production and storage of products. Numerical calculations are carried out on a computer using the described problem-solving algorithm in which it is possible to take into account restrictions on the values of controls. Optimal values are determined and appropriate schedules of the production plan, storage of products and limited management at discrete instants of time are constructed.DOI: http://dx.doi.org/10.5755/j01.itc.47.4.19933

A new concept of system equivalence which allows the establishment of a formal relation between singular and regular systems has been introduced. By applying this concept, an open-loop strategy for finite-time control of a given solvable singular system, which is simple for both computation and implementation, is developed. A strategy for finite-time output feedback control is considered for a continuous singular system. It is shown that provided the system is observable, a desired polynomial command for finite-time control can be determined from a finite sequence of output measurements sampled at discrete instants of time.

In this work we address the problem of performing a repetitive task when we have uncertain observations and dynamics. We formulate this problem as an iterative infinite horizon optimal control problem with output feedback. Previously, this problem was solved for linear time-invariant (LTI) system for the case when noisy full-state measurements are available using a robust iterative learning control framework, which we refer to as robust learning-based model predictive control (RL-MPC). However, this work does not apply to the case when only noisy observations of part of the state are available. This limits the applicability of current approaches in practice: First, in practical applications we typically do not have access to the full state. Second, uncertainties in the observations, when not accounted for, can lead to instability and constraint violations. To overcome these limitations, we propose a combination of RL-MPC with robust output feedback model predictive control, named robust learning-based output feedback model predictive control (RLO-MPC). We show recursive feasibility and stability, and prove theoretical guarantees on the performance over iterations. We validate the proposed approach with a numerical example in simulation and a quadrotor stabilization task in experiments.

We present an approach for the coordination of a network of agents in a cyber-physical environment. The agents's dynamics are nonlinear, of arbitrary dimensions and possibly heterogeneous. The objective is to design resource-aware distributed control strategies to ensure a coordination task. In particular, we aim at ensuring the convergence of the differences between the agents' output variables to a prescribed compact set, hence covering rendez-vous and formation control as specific scenarios. We develop event-based sampling strategies for that purpose. Three scenarios are studied. We first focus on event-triggered control, in which case the agents continuously measure the relative distances with their neighbours and only update their control input at some time instants. This set-up is relevant to limit changes in control signals and therefore to reduce the resources usage of the actuators. A triggering rule is defined for each edge using an auxiliary variable, whose dynamics only depends on the local variables. We then explain how to derive time-triggered and self-triggered distributed controllers. These control strategies collect measurements and update the control inputs only at some discrete time instants, which save communication and computation resources. The existence of a uniform minimum amount of times between any two edge events is guaranteed in all cases, thus ruling out Zeno phenomenon. The analysis is carried out within the framework of hybrid systems and an invariance principle is used to conclude about coordination.