An improved output feedback controller design for linear discrete‐time systems using a matrix decomposition method

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PurposeThe purpose of this paper is to propose a decentralized output feedback controller for cooperative attitude regulation of spacecraft formation in absence of angular velocity feedback.Design/methodology/approachThe nonlinear relative attitude dynamic and kinematic equations represented by relative quaternion and relative angular velocity, respectively, are considered in this paper. The lead filter is employed to synthesize virtual angular velocity signal so that the design of output feedback controller is achieved. Lyapunov method is adopted to prove the stability of closed‐loop system. Considering the external disturbance, the theory of L2‐gain disturbance attenuation is employed to improve the designed controller. Numerical simulations are carried out to verify the controllers proposed.FindingsIt is found that the closed‐loop system can be guaranteed asymptotically stable in absence of external disturbance. When disturbance is considered, as long as the sufficient condition proposed is satisfied, the improved controller can render system uniformly ultimately bounded stable.Practical implicationsThe proposed output feedback control scheme can be considered as a fall‐back alternative for the case that the angular velocity sensors fail, or seen as another option for the system without angular velocity sensors at all.Originality/valueUnlike most classical works in the field of output feedback which focus on centralized scheme and neglect the disturbance, the controller proposed in this paper is able to handle the output feedback control problem of multi‐agent formation in a decentralized fashion, so as to avoid the single failure point of a centralized scheme. Meanwhile, the capability of L2‐gain disturbance attenuation is also achieved simultaneously.

Global stabilization for linear continuous time-varying systems

This paper considers linear time-invariant control systems over fading channels in both continuous-time and discrete-time cases and addresses the design of output feedback controllers that stabilize the closed-loop system in the mean square sense. It is shown that a sufficient and necessary condition for the existence of such controllers can be obtained by solving a convex optimization problem in the form of a semidefinite program. This condition is obtained by reformulating mean square stability as asymptotical stability of a suitable matrix comprising plant, controller, and channel, and by introducing modified Hurwitz and Schur stability criteria.

This paper is concerned with the output feedback control problem for a class of nonlinear system with time delay. First, a state feedback controller is design and a sufficient condition with exponential stability is obtained. Second, we study the observer design problem. And we proved that the observer designed in this paper ensure the observation error exponential converge to zero. Furthermore, output feedback controller using state feedback control and observer design is studied.

A novel neural network (NN) -based output feedback controller with magnitude constraints is designed to deliver a desired tracking performance for a class of multi-input-multi-output (MIMO) discrete-time strict feedback nonlinear systems. Reinforcement learning in discrete time is proposed for the output feedback controller, which uses three NN: 1) a NN observer to estimate the system states with the input-output data; 2) a critic NN to approximate certain strategic utility function; and 3) an action NN to minimize both the strategic utility function and the unknown dynamics estimation errors. The magnitude constraints are manifested as saturation nonlinearities in the output feedback controller design. Using the Lyapunov approach, the uniformly ultimate boundedness (UUB) of the state estimation errors, the tracking errors and weight estimates is shown.

This work considers the design of optimal static output feedback controllers with priori structural constraints for linear systems. The structural constraints impose individual elements of the feedback matrix to satisfy certain equality or inequality constraints. The barrier method is used to address an auxiliary minimization problem to attain an approximate solution to the original nonconvex constrained optimization problem. The Lagrange multiplier method is applied to derive necessary conditions for the optimal solution. An easy-to-implement algorithm based on the gradient descent method is developed to solve the auxiliary minimization problem, and the convergence of the algorithm is proven. The effectiveness of the proposed methodology is validated using two numerical examples.

This paper proposes guaranteed cost design of robust output feedback controller for continuous linear parametric uncertain systems. New necessary and sufficient conditions for static output feedback stabilizability of linear continuous time systems underly the design procedure. Proposed algorithms are computationally simple and tightly connected with the Lyapunov stability theory and the LQR optimal state feedback design. The proposed approach allows for prescribing the structure of the output feedback gain matrix (including the decentralized one) by the designer. New design method proposed in this paper, exploit genetic algorithm to design robust controller with guaranteed cost for polytopic linear continuous time systems. Numerical example is given to illustrate the performance of the proposed robust controller.

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.

In this paper, a new continuous output feedback control mechanism is developed for output tracking for a class of high-order multi-input nonlinear systems with an input gain matrix that is positive definite but non-symmetric. The controller yields semiglobal uniformly ultimately bounded (SGUUB) tracking while compensating for unstructured uncertainty in both the drift vector and the input matrix. First, a fullstate feedback controller is designed based on limited assumptions on the structure of the system nonlinearities and the controller is proven to yield SGUUB tracking through a Lyapunov-based analysis. Then, an output feedback control design based on a high gain observer is proposed. A comprehensive stability analysis of the closed-loop system under output feedback is carried out and a recovery of the state feedback SGUUB result is demonstrated for the output feedback control system. Neural network estimation method is employed in both state and output feedback control design to feedforward compensate for the nonlinear system uncertainty.

Rbust control of linear systems with real parametric uncertainty

Positive real control for 2-D discrete delayed systems via output feedback controllers

In this paper, a robust method for the simultaneous coordinated design of the interline power flow controller (IPFC) and power system stabilizer (PSS) based on output feedback controllers in a single-machine infinite-bus power system for the enhancement of power systems low-frequency oscillations damping is presented. The Honey Bee Algorithm, which has a strong ability to find the most optimistic results, is employed to search for optimal IPFC and PSS output feedback controller parameters. A singular value decomposition method is utilized to select the most effective damping control signal of the IPFC output feedback controller. To assess the effectiveness and robustness of the proposed method, simulation studies are carried out for three operating conditions. Analysis of the results shows that the combined design has an excellent capability for damping a power system’s low-frequency oscillations. Moreover, system performance analysis under different operating conditions and performance indices shows the effectiveness of the proposed method even when a severe fault is applied.

Design of Robust PID Controller using Static Output Feedback framework

This paper considers dynamical compensators design for purpose of pole assignment for discrete-time linear periodic systems. Similar to linear time-invariant systems, it is pointed out that the design of a periodic dynamical compensator can be converted into the design of a periodic output feedback controller for an augmented system. Utilizing the recent result on output feedback pole assignment, parametric solutions for this problem are obtained. The design approach can be used as a basis for the robust dynamical compensator design for this type of systems. Combined with a robustness index presented in this paper, robust dynamical compensator design problem is converted into a constrainted optimization problem. A numerical example is employed to illustrate the validity and feasibility of the methods.