Academic literature on the topic 'Optimal LQG control under random delays'

This paper studies the agent identity privacy problem in the scalar linear quadratic Gaussian (LQG) control system. The agent identity is a binary hypothesis: Agent A or Agent B. An eavesdropper is assumed to make a hypothesis testing the agent identity based on the intercepted environment state sequence. The privacy risk is measured by the Kullback–Leibler divergence between the probability distributions of state sequences under two hypotheses. By taking into account both the accumulative control reward and privacy risk, an optimization problem of the policy of Agent B is formulated. This paper shows that the optimal deterministic privacy-preserving LQG policy of Agent B is a linear mapping. A sufficient condition is given to guarantee that the optimal deterministic privacy-preserving policy is time-invariant in the asymptotic regime. It is also shown that adding an independent Gaussian random process noise to the linear mapping of the optimal deterministic privacy-preserving policy cannot improve the performance of Agent B. The numerical experiments justify the theoretic results and illustrate the reward–privacy trade-off.

By multi-rate networked control systems (NCS), we mean the sampling periods of the sensor, the controller and the actuator in networked control systems are not the same, that is to say there are more than one sampling rate in networked control systems. For the long time delay multi-rate NCS with event-driven controller and actuator, a stochastic discrete model is established under operator. The state feedback control laws for the multi-rate NCS in operator domain are designed by using a dynamic programming approach. The derived optimal LQG controller can be used as a delay-compensator for multi-rate NCS with long time delays. An example is given to verify the theory results of this paper.

To improve the ride comfort of electric vehicle, the vertical dynamic model of electric vehicle is established under the excitation of road surface and wheel hub motor. The road excitation is divided into random continuous road and convex road, and the influence of motor electromagnetic excitation on vibration is analyzed. To avoid the empirical value influence of each index weight coefficient on the main vibration control, the weight coefficient is determined by analytic hierarchy process (AHP), the LQG controller of vehicle active suspension is designed by using optimal control theory, and the comprehensive optimization of performance index is realized. The effectiveness of control effect is verified by comparing active and passive control based on single and double excitation.

Modern tall buildings use lighter construction materials that have high strength and less stiffness and are more flexible. Although this results in the improvement of structural safety, excessive wind-induced excitations could lead to occupant discomfort. The optimal control law of a linear quadratic Gaussian (LQG) controller with an active tuned mass damper (ATMD) is used for reducing the along-wind response of a tall building. ATMD consists of a second mass with optimum parameters for tuning frequency and damping ratio of the tuned mass damper (TMD), under the stationary random load, was used. A fluctuating along-wind load, acting on a tall building, was treated as a stationary Gaussian white noise and was simulated numerically, in the time domain, using the along-wind load spectra proposed by G. Solari in 1993. Using this simulated wind load, it was possible to calculate the along-wind responses of a tall building (with and without the ATMD), using an LQG controller. Comparing the RMS (root mean square) response revealed that the numerically simulated along-wind responses, without ATMD, are a good approximation to the closed form response, and that the reduced responses with ATMD and LQG controller were estimated by varying the values of control design parameters.

This study formulates a dynamical system for the control of a single product inventory system in accordance with the random value of demand and the percentage of damaged product during the delivery process. The formulated model has the form of a linear state-space system comprising of two disturbances, which represents the random value of demand and the percentage of the damaged product during delivery. The optimal value of the product amount ordered to the supplier is properly calculated by using the linear quadratic gaussian (LQG) method. The controller is used by the manager to make inventory level decisions under the uncertainty of demand and damaged items during the product delivery process. The result showed that the optimal product order for each review time was achieved, and the inventory level was used to obtain the right set point properly. Moreover, based on comparison with other research results, the proposed model was well performed.

The vibration suppression of structures using a semi-active mass damper is investigated in this study. A magnetorheological (MR)-damper is utilized to design the semi-actively controlled mass damper. The inverse MR-damper model is developed on the basis of an improved LuGre friction model, and combined with a designed H2/Linear-Quadratic-Gaussian (H2/LQG) controller, in order to control the command current of the MR-damper to suppress structural vibration levels effectively. Illustrated examples are considered to investigate the vibration suppression effectiveness of a semi-active mass damper with a MR-damper, using the developed control methodology. The simulation results were compared with those reported in literature in order to validate the presented methodology.

A general approach to self-learning based on the ideas of adaptive (dual) control is presented. This means that we consider the control problem for a stochastic system with uncertainty as a leading example. Some system’s parameters are unknown and modeled as random variables with known a’priori distribution function. To optimize an objective function, a controller has to learn the system’s parameter values. The main difficulty comes from the fact that he has to optimize the objective function parallely, i.e., at the same time. Moreover, these two goals considered separately not necessarily coincide and the main problem in the adaptive control is to find the trade-off between them. Looking from the self-learning perspective the two directions are visible. The first is to extract the learning procedure from an optimal adaptive control law and to formulate it as a Cybernetic Principle of self-learning. The second is to consider a control problem with the special objective function. This function has to measure our knowledge about unknown parameters. It can be the Fisher information (Banek & Kulikowski, 2003), the joint entropy (for example Saridis, 1988; Banek & Kozlowski, 2006), or something else. This objective function in the control problem will force a controller to steer a system along trajectories that are rich in information about unknown quantities. In this chapter the authors follow the both directions. First they obtain conditions of optimality for a general adaptive control problem and resulting algorithm for computing extremal controls. The results are then applied to the simple example of the Linear Quadratic Gaussian (LQG) problem. By using analytical results and numerical simulations the authors are able to show how control actions depend on the a’piori knowledge about a system. The first conclusion is that a natural, methodological candidate for the optimal self-learning strategy, the “certainty equivalence principle”, fails to satisfy optimality conditions. Optimal control obtained in the case of perfect system’s knowledge is not directly usable in the partial information case. The need of active learning is an essential factor. The differences between controls mentioned above are visible on a level of computations and should be interpreted on a higher level of cybernetic thinking in order to give a satisfactory explanation, perhaps in the form of another principle. Under absence of the perfect knowledge of parameters values, the control actions are restricted by some measurability requirement and the authors compute the Lagrange multiplier associated with this “information constraint”. The multiplier is called a “dual” or “shadow” price and in the literature of the subject is interpreted as an incremental value of information. The authors compute the Lagrange multiptier and analyze its evolution to see how its value changes as the time goes on. As a second sort of conclusion the authors get the self-learning characteristic coming from the information theory point of view. In the last section the authors follow the second direction. In order to estimate the speed of self-learning they choose as an objective function, the conditional entropy. They state the optimal control problem for minimizing the conditional entropy of the system under consideration. Using general results obtained at the beginning, they get the conditions of optimality and the resulting algorithm for computing the extremal controls. Optimal evolution of the conditional entropy tells much about intensivity of self-learning and its time distribution.