Control of a hysteresis model subject to random failures

The note presents conditions to assure weak stability in the mean for a hysteresis Bouc-Wen model controlled by a proportional-integral controller subject to random failures. When a failure happens, the controller turns off and remains off for a while. After that the controller turns on and keeps on until the occurrence of the next failure. The failures occur according to a Poisson distributed process. A numerical example illustrates the result

Stationary policies for the second moment stability in a class of stochastic systems

This paper presents a study on the uniform second moment stability for a class of stochastic control system. The main result states that the existence of the long-run average cost under a stationary policy is equivalent to the uniform second moment stability of the corresponding stochastic control system. To illustrate the result, a numerical example is developed to verify the uniform second moment stability of a simultaneous state-feedback control system

Almost periodic parameters for the second moment stability of linear stochastic systems

The technical note presents conditions to assure the uniform second moment stability for a class of linear time-varying stochastic systems. The system parameters are assumed to be almost periodic, a concept that is weaker than the periodic one. Under the existence of the long-run average cost associated with the stochastic system, we apply the almost periodicity to prove the desired stability result. An application illustrates the usefulness of the approach by implementing an almost periodic state-feedback strategy to control the velocity of a DC motor device

On the numerical solution of the control problem of switched linear systems

This paper presents a method to compute an epsilon-optimal solution of the control problem of switched linear systems. A difficulty that emerges in the evalution of the optimal solution is that the cardinality of the solution set increases exponentially as long as the time-horizon increases linearly, which turns the problemintractable when the horizon is sufficiently large. We propose a numerical method to overcome such difficulty, in the sense that our approach allows the evalution of epsilon-optimal solutions with corresponding sets that do not increase exponentially

Second moment constraints and the control problem of Markov jump linear systems

This paper addresses the optimal solution for the regulator control problem of Markov jump linear systems subject to second moment constraints. We can characterize and obtain the solution explicitly using linear matrix inequalities techniques. The constraints are imposed on the second moment of both the system state and control vector, and the optimal solution is obtained in a computable form. To illustrate the usefulness of the approach, specially that for systems subject to abrupt variations and physical limitations, we present an application for one joint of the European Robotic Arm

On the control of Markov jump linear systems with no mode observation: Application to a DC Motor device

This paper deals with the control problem of discrete-time Markov jump linear systems for the case in which the controller does not have access to the state of the Markov chain. A necessary optimal condition, which is nonlinear with respect to the optimizing variables, is introduced, and the corresponding solution is obtained through a variational convergent method. We illustrate the practical usefulness of the derived approach by applying it in the control speed of a real DC Motor device subject to abrupt power failures

Mode-independent H2-control of a DC motor modeled as a Markov jump linear system

This brief presents a control strategy for Markov jump linear systems (MJLS) with no access to the Markov state (or mode). The controller is assumed to be in the linear state-feedback format and the aim of the control problem is to design a static mode-independent gain that minimizes a bound to the corresponding H2 -cost. This approach has a practical appeal since it is often difficult to measure or to estimate the actual operating mode. The result of the proposed method is compared with that of a previous design, and its usefulness is illustrated by an application that considers the velocity control of a DC motor device subject to abrupt failures that is modeled as an MJLS

A Systematization of the Unscented Kalman Filter Theory

In this paper, we propose a systematization of the (discrete-time) Unscented Kalman Filter (UKF) theory. We gather all available UKF variants in the literature, present corrections to theoretical inconsistencies, and provide a tool for the construction of new UKF's in a consistent way. This systematization is done, mainly, by revisiting the concepts of Sigma-Representation, Unscented Transformation (UT), Scaled Unscented Transformation (SUT), UKF, and Square-Root Unscented Kalman Filter (SRUKF). Inconsistencies are related to 1) matching the order of the transformed covariance and cross-covariance matrices of both the UT and the SUT; 2) multiple UKF definitions; 3) issue with some reduced sets of sigma points described in the literature; 4) the conservativeness of the SUT; 5) the scaling effect of the SUT on both its transformed covariance and cross-covariance matrices; and 6) possibly ill-conditioned results in SRUKF's. With the proposed systematization, the symmetric sets of sigma points in the literature are formally justified, and we are able to provide new consistent variations for UKF's, such as the Scaled SRUKF's and the UKF's composed by the minimum number of sigma points. Furthermore, our proposed SRUKF has improved computational properties when compared to state-of-the-art methods

Gradient-based optimization techniques for the design of static controllers for Markov jump linear systems with unobservable modes

The paper formulates the static control problem of Markov jump linear systems, assuming that the controller does not have access to the jump variable. We derive the expression of the gradient for the cost motivated by the evaluation of 10 gradient-based optimization techniques. The numerical efficiency of these techniques is verified by using the data obtained from practical experiments. The corresponding solution is used to design a scheme to control the velocity of a real-time DC motor device subject to abrupt power failures

Control of temperature to suppress the population of Rhyzopertha dominica (F.) (Coleoptera, Bostrichidae) in a grain silo prototype

This note presents some results from laboratory experiments that were conducted to characterize the influence of temperature in the mortality of adults of the insect known as lesser grain borer, Rhyzopertha dominica (F.). The insects were separated into strains and were appropriately immersed into a mass of wheat, and the infested wheat was stored in a silo bin of small dimensions with control of temperature. Our experiments indicates that the control of temperature can be used as a successful tool to increase the mortality of R. dominica in grain silos. The paper also describes the construction of the electrical device that implements the control of temperature in the proposed grain silo prototype