Output mini-max control for polynomial systems: Analysis and application

In this paper, we present a solution to the problem of the quadratic Mini-Max regulator for polynomial uncertain systems. The main characteristic of this type of problems is that the parameters describing the dynamic of the nonlinear plant depend on a vector of unknown parameters, which belongs to a finite parametric set, and the solution is given in terms of the worst case scenario. That is to say, the result of the application of a certain control input (in terms of the cost function value) is associated with the worst or least favorable value of the unknown parameter. Based on the general necessary conditions for mini-max optimality, a closed form for the control is provided, which makes use of a p-linear form tensor representation of the polynomial system. In its turn, this allows one to present the solution in a way similar to the so called Riccati technique. The final control is shown to be a convex combination (with some weights) of the optimal controls for each fixed parameter of the polynomial system. A numerical example for the robust regulation of the well-known Duffing equation which represents a typical (and challenging to control) nonlinear polynomial system is presented, to show the effectiveness of our approach.

Adaptive signal processing algorithms are often used in order to track an unknown time-varying parameter vector. This work develops an upper bound on the mean of the norm-squared error between the unknown parameter vector being tracked and the value obtained by the algorithm. The results require very mild covariance decay rate conditions on the training data and a bounded algorithm. The upper bound illustrates the relationship between the algorithm step size and the maximum rate of variation in the parameter vector being tracked.

This paper proposes a new algorithm for achieving discrete-time sliding mode for single input single output systems with bounded matched uncertainty using output feedback. The concept of periodic output feedback is used here. It has been shown that, when the output of the uncertain system with matched uncertainty is sampled slower than the input, there exist a discrete-time quasi sliding mode. The method is very general and is applicable to any controllable and observable linear time invariant single input single output system. The proposed technique is illustrated with numerical examples.

The iterative method, which can be applied to estimation of the unknown vector of discrete parameters in combination with filtering of the unknown vector of continuous signal parameters, is proposed. It is demonstrated that this method makes it possible to construct highly efficient algorithms for joint demodulation and filtering of communications channel parameters in code-division multiple-access and orthogonal frequency-division multiplexing systems.

Robust and risk sensitive control of discrete time, finite state systems on an infinite horizon is considered, with either state or output feedback. The solution of the state feedback robust control problem is characterized in terms of the value of an average cost dynamic game. The risk sensitive stochastic optimal control problem is solved using the policy iteration algorithm, and the optimal rate is expressed in terms of the value of a stochastic dynamic game with average cost per unit time criterion. By taking a small noise limit a deterministic dynamic game is obtained, which is closely related to the robust control problem. For the problem with output feedback (partial state information) the analysis depends on introducing appropriate information states for the risk sensitive and robust control problems.

In this paper we construct an algorithm of successive approximation type that computes a locally optimal periodic policy for a Markov decision chain with partial state information. The algorithm is applied to a queueing network with server control.

A discrete-event system (DES) is described by a state-transition model. By disabling and enabling controllable events according to a rule based on partial information about the current state of the system, a static state-feedback controller synthesizes a predicate specifying states reachable from the initial state in the controlled system. Concepts of controllable predicate and observable predicate are introduced. It is shown that a predicate can be synthesized by a static state-feedback controller utilizing only partial state information if and only if the predicate is both controllable and observable. Some general results are presented for a state-variable model of a controlled DES.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A robust output feedback control which globally stabilizes a class of SISO minimum-phase nonlinear systems with known and constant relative degree containing a vector of unknown parameters is developed. The constant parameter vector is not restricted to enter linearly in the state equations but it is assumed to belong to a known compact set and an imprecise knowledge of the nonlinearities (e.g., lookup tables) is allowed. The class of nonlinear systems is determined by geometric conditions; an additional assumption, which generalizes the knowledge of the sign of high-frequency gain for linear systems, is also required. The nonlinearities are restricted to depend, in suitable coordinates, on the output only: no growth conditions, such as sector or Lipschitz, are required. The robust output feedback control stabilizes the system for every value of the parameter vector in a known compact set. The order of the compensator is equal to the relative degree minus one. >

A channel model for channels with unknown state and partial state information available causally at the decoder is proposed. The model is based on arbitrarily varying channels (AVCs), and the partial state information is characterized by allowing the decoder to know a subset in which the average empirical channel must lie. A randomized rateless coding scheme for these channels is presented that achieves rates near that if the channel quality were known in advance under the assumption that the average channel can be estimated accurately. The same coding scheme can use used to multicast a common message to several receivers with different state sequences.

A stochastic adaptive control problem where complete state information is not available to the controller is considered. The system is modeled as a finite stochastic automaton. These models are a slight generalization of the more common partially observable controlled Markov chain models.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Event-triggered robust cooperative output regulation for a class of linear multi-agent systems with an unknown exosystem

Let \( \{ ({x'_i},{y_i})\} _{i = 1}^N \) be an iid sample drawn from a known distribution F(x i,y i, s), where s is a k × 1 vector of unknown parameters. Let f y|x (y, β) denote the likelihood function of y | x, which is the density function of y | x if y |x is continuous or the probability of y | x if y | x is discrete. Define f x (x) analogously, which is not a function of s.

The paper considers the problem of estimating the parameters in a continuous time regression model with a non-Gaussian noise of pulse type. The vector of unknown parameters is assumed to belong to a compact set. The noise is specified by the Ornstein–Uhlenbeck process driven by the mixture of a Brownian motion and a compound Poisson process. Improved estimates for the unknown regression parameters, based on a special modification of the James–Stein procedure with smaller quadratic risk than the usual least squares estimates, are proposed. The developed estimation scheme is applied for the improved parameter estimation in the discrete time regression with the autoregressive noise depending on unknown nuisance parameters.

On best unbiased prediction and its relationships to unbiased estimation

: The general multiplicative model represents the hazard function as the product of an 'underlying hazard rate, gamma (t), of unspecified form and a certain function of known form, g(z; beta), where z is a vector of concomitant variables, and Beta is a vector of unknown parameters. Assuming that gamma (t) can be approximated by a constant between any two consecutive failures, the general forms of likelihood function are derived. The likelihood utilizes the available information on the time of exposure to risk of each individual (until failure or withdrawal). Special cases, when the z's do not depend on t are discussed in some detail. Multiple failures are handled in a simple manner - no ordering of failures is required. Estimation of empirical survival function when there are no covariates is discussed. An example using heart transplant data, is given (for illustrative purpose only).