Closed-Loop Strategy for Stackelberg Game Problem with Incomplete Information Structures

Output feedback Q-learning for discrete-time linear zero-sum games with application to the H-infinity control

This paper presents an output feedback design approach based on the adaptive control scheme developed for nonlinearly parameterized systems, to achieve global output regulation for a class of nonlinear systems in output feedback form. We solve the output regulation problem without the knowledge of the sign and the value of the high frequency gain a priori. It is not necessary to have both the limiting assumptions that the exogenous signal w and the unknown parameter μ belong to a prior known compact set and the high frequency gain has a determinate lower and upper bounds. The effectiveness of the proposed algorithm is shown with the help of an example.

Adaptive control for output feedback nonlinear systems in the presence of modeling errors

This paper considers the output feedback adaptive controller design problem for a class of discrete-time nonlinear systems in output feedback form with unknown control directions and preceded by unknown hysteresis. The problem of lacking in a-priori knowledge on the control directions and unknown hysteresis are solved by using the discrete Nussbaum gain and Prandtl–Ishlinskii model, respectively. The system is transformed into the form of a nonlinear auto regressive moving average (NARMA) model to construct an output feedback control. To overcome the noncausal problem in the control design, future output prediction laws and parameter update laws with the dead-zone technique are constructed on the basis of the NARMA model. The proposed control algorithm guarantees that all the signals in the controlled system are bound and the output tracking error is made to be neighbourhood around zero, ultimately. Finally, simulations are performed on a nonlinear system to show the effectiveness of the proposed method

Rotating stall and surge have been stabilized in a transonic single-stage axial compressor using active feedback control. The control strategy is to sense upstream wall static pressure patterns and feed back the signal to an annular array of twelve separately modulated air injectors. At tip relative Mach numbers of 1.0 and 1.5 the control achieved 11 and 3.5 percent reductions in stalling mass flow, respectively, with injection adding 3.6 percent of the design compressor mass flow. The aerodynamic effects of the injection have also been examined. At a tip Mach number, Mtip, of 1.0, the stall inception dynamics and effective active control strategies are similar to results for low-speed axial compressors. The range extension was achieved by individually damping the first and second spatial harmonics of the prestall perturbations using constant gain feedback. At a Mtip of 1.5 (design rotor speed), the prestall dynamics are different than at the lower speed. Both one-dimensional (surge) and two-dimensional (rotating stall) perturbations needed to be stabilized to increase the compressor operating range. At design speed, the instability was initiated by approximately ten rotor revolutions of rotating stall followed by classic surge cycles. In accord with the results from a compressible stall inception analysis, the zeroth, first, and second spatial harmonics each include more than one lightly damped mode, which can grow into the large amplitude instability. Forced response testing identified several modes traveling up to 150 percent of rotor speed for the first three spatial harmonics; simple constant gain control cannot damp all of these modes and thus cannot stabilize the compressor at this speed. A dynamic, model-based robust controller was therefore used to stabilize the multiple modes that comprise the first three harmonic perturbations in this transonic region of operation.

In this work, the problem of stabilizing a discrete stochastic-parameter system with incomplete state information is addressed. In order to solve this problem, a time-invariant compensator system composed of a constant gain observer and a constant feedback gain, is proposed. The stabilizability conditions depend both on the first and second moments of the stochastic parameters.

Output feedback form of Chua’s circuit and modular adaptive control of chaos using single measurement

This paper studies the cooperative global robust output regulation problem for the nonlinear multi-agent systems in output feedback form with relative degree $r=2$ subject to arbitrarily large uncertainty. The robust control method alone cannot handle arbitrarily large uncertainty. By combining the robust and adaptive high gain technique, we develop a recursive procedure to construct a distributed output feedback control law to deal with the problem. The theoretical result of this paper is applied to the leader-following consensus problem of a family of hyper-chaotic Lorenz systems.

In this paper, we study the cooperative global robust output regulation problem for nonlinear multi-agent systems in output feedback form with any relative degree subject to switching networks. After establishing two lemmas to lay the foundation for constructing a switching control law, we present the solvability conditions of our problem via the multiple Lyapunov functions and average dwell time method.

Decentralized Stackelberg Strategies for Interconnected Stochastic Dynamic Systems

This paper presents a Fuzzy Mathematical Programming (FMP) approach for solving Multilevel Decentralized Programming Problems (ML(D)PPs). The higher level Decision Maker(DM) makes the decision first to provide preferred values of the decision variables under control and the follower reacts by optimizing the objective function conditioned on the higher level DM’s decision. A simple method is employed to find a satisfactory solution under fuzziness with linear fractional objectives overcoming the selection of membership functions and tolerance values and terminates in a finite number of steps. The methodology proposes small number of iterations and aims at reducing the feasible space of a decision variable at each level of the hierarchical system until a satisfactory solution is obtained at the last level. The Stackelberg strategy is employed as a solution concept when decision problems are modeled as two-level programming problems, whether there is a cooperative relationship between the decision makers or not. Illustrative numerical example is provided to demonstrate the feasibility of the proposed method.

We investigate the impact of Stackelberg routing to reduce the price of anarchy in network routing games. In this setting, an α fraction of the entire demand is first routed centrally according to a predefined Stackelberg strategy and the remaining demand is then routed selfishly by (nonatomic) players. Although several advances have been made recently in proving that Stackelberg routing can, in fact, significantly reduce the price of anarchy for certain network topologies, the central question of whether this holds true in general is still open. We answer this question negatively by constructing a family of single-commodity instances such that every Stackelberg strategy induces a price of anarchy that grows linearly with the size of the network. Moreover, we prove upper bounds on the price of anarchy of the largest-latency-first (LLF) strategy that only depend on the size of the network. Besides other implications, this rules out the possibility to construct constant-size networks to prove an unbounded price of anarchy. In light of this negative result, we consider bicriteria bounds. We develop an efficiently computable Stackelberg strategy that induces a flow whose cost is at most the cost of an optimal flow with respect to demands scaled by a factor of 1 + √1−α. Finally, we analyze the effectiveness of an easy-to-implement Stackelberg strategy, called SCALE. We prove bounds for a general class of latency functions that includes polynomial latency functions as a special case. Our analysis is based on an approach that is simple yet powerful enough to obtain (almost) tight bounds for SCALE in general networks.

Optimal State-Linear Filtering Through Implicit Output Equation

This article investigates the problem of global neural network (NN) tracking control for uncertain nonlinear systems in output feedback form under disturbances with unknown bounds. Compared with the existing NN control method, the differences of the proposed scheme are as follows. The designed actual controller consists of an NN controller working in the approximate domain and a robust controller working outside the approximate domain, in addition, a new smooth switching function is designed to achieve the smooth switching between the two controllers, in order to ensure the globally uniformly ultimately bounded of all closed-loop signals. The Lyapunov analysis method is used to strictly prove the global stability under the combined action of unmeasured states and system uncertainties, and the output tracking error is guaranteed to converge to an arbitrarily small neighborhood through a reasonable selection of design parameters. A numerical example and a practical example were put forward to verify the effectiveness of the control strategy.

This paper focuses on the problem of quadratic dissipative control for linear systems with or without uncertainty. We consider the design of feedback controllers to achieve (robust) asymptotic stability and strict quadratic dissipativeness. Both linear static state feedback and dynamic output feedback controllers are considered. First, the equivalence between strict quadratic dissipativeness of linear systems and a H performance is established. Necessary and sufficient conditions for the solution of the quadratic dissipative control problem are then obtained using a linear matrix inequality (LMI) approach. As for uncertain systems, we consider structured uncertainty characterized by a dissipative system. This uncertainty description is quite general and contains commonly used types of uncertainty, such as norm-bounded and positive real uncertainties, as special cases. It is shown that the robust dissipative control problem can be solved in terms of a scaled quadratic dissipative control problem without uncertainty. LMIbased methods for designing robust dissipative controllers are also derived. The results of this paper unify existing results on H and positive real control and provide a more flexible and less conservative robust control design as it allows for a better trade-off between phase and gain performances.