Reference output tracking control for a flexible air‐breathing hypersonic vehicle via output feedback

This paper addresses the problem of reference output tracking control for the longitudinal model of a flexible air‐breathing hypersonic vehicle (FAHV) by utilizing the output feedback control approach. The dynamic characteristics of the FAHV along with the aerodynamic effects of hypersonic flight make the flight control of such systems highly challenging. Moreover, there exist some intricate couplings between the engine and flight dynamics as well as complex interaction between rigid and flexible modes in the longitudinal model. These couplings bring difficulty to the flight control design for the intractable hypersonic vehicle systems. This paper deals with the problem of reference output tracking control for the longitudinal model of the FAHV. By utilizing the trim condition information including the state of altitude, velocity, angle of attack, pitch angle, pitch rate and so on, the linearized model is established for the control design objective. Then, the reference output velocity and altitude tracking control design problem is proposed for the linearized model. The flexible models of the FAHV system are hardly measured because of the complex dynamics and the strong couplings of the FAHV. Thus, by using only limited flexible model information, the reference output tracking performance analysis criteria are obtained via Lyapunov stability theory. Then, based on linear matrix inequality optimization algorithm, the static output feedback controller is designed to stabilize the closed‐loop systems, guarantee a certain bound for the closed‐loop value of the cost function, and can make the control output achieve the reference velocity and altitude tracking performance. Subsequently, the condition of dynamic output feedback controller synthesis is given in terms of linear matrix inequalities and a numerical algorithm is developed to search for a desired dynamic output feedback controller which minimizes the cost bound and obtains the excellent reference altitude and velocity tracking performance simultaneously. The effectiveness of the proposed reference output tracking control method is demonstrated in simulation part. Furthermore, the superior reference velocity and altitude performance commands could be achieved via using static and dynamic output feedback controllers under lacking some unmeasured flexible states information in the measurement output vector. Copyright © 2011 John Wiley & Sons, Ltd.     

Suboptimal digital LQ output feedback control design via LMI relaxations

This paper deals with suboptimal linear quadratic (LQ) output feedback control of linear discrete systems. It is shown that degree of freedoms by instrumental variables employed in this paper lead to much flexibility in obtaining a suboptimal LQ controller. An improved convex optimization method involving linear matrix inequalities (LMIs) is suggested to solve the matrix inequalities characterizing a solution of the suboptimal LQ problem. Of the major interest of this paper is an extension to a class of nonconvex LQ problems of large size arising in decentralized feedback, simultaneous control, periodic feedback control, etc. Illustrative examples demonstrate the validity of the proposed convex approximate approach to optimal LQ output feedback control. Also, it is shown that suboptimal LQ solutions obtained by the proposed method can be used as an initial feasible point of existing iterative LMI algorithms to improve the feasibility of the iterative methods. Copyright © 2007 John Wiley & Sons, Ltd.     

Mixed H2/H∞ robust output feedback sliding mode control

This paper presents an output feedback sliding mode control scheme for uncertain dynamical systems. The design problem is solved in two steps, involving first a state feedback and then an output feedback problem. First, using the null space dynamics, the sliding surface for the unmatched uncertainty is designed. Then, by tuning the sliding surface, a robust controller is constructed for the whole uncertainty; this problem takes the form of static‐output feedback. Based on this, a dynamic output feedback controller for the system augmented with the sliding surface is designed. The synthesis involves the solution of an Linear Matrix Inequality (LMI) and Bilinear Matrix Inequality (BMI) problem; the BMI problem is solved iteratively. The proposed approach is illustrated by applying it to a well‐known robust benchmark problem and also experimentally on a spring mass system with variable stiffness. Simulation and experimental results show that the proposed method outperforms previous approaches in terms of robust performance. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust ℋ︁2 static output feedback design starting from a parameter‐dependent state feedback controller for time‐invariant discrete‐time polytopic systems

This paper investigates the problem of computing robust ??₂ static output feedback controllers for discrete‐time uncertain linear systems with time‐invariant parameters lying in polytopic domains. A two stages design procedure based on linear matrix inequalities is proposed as the main contribution. First, a parameter‐dependent state feedback controller is synthesized and the resulting gains are used as an input condition for the second stage, which designs the desired robust static output feedback controller with an ??₂ guaranteed cost. The conditions are based on parameter‐dependent Lyapunov functions and, differently from most of existing approaches, can also cope with uncertainties in the output control matrix. Numerical examples, including a mass–spring system, illustrate the advantages of the proposed procedure when compared with other methods available in the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

Design of ℋ︁∞ fuzzy controllers for nonlinear systems with random data dropouts

The problem of ??_∞ control of nonlinear networked control systems subject to random data dropout is concerned in this paper. The random data dropout, because of the limited bandwidth of the network channels, could exist in the communication channels both from the sensor to the controller and from the controller to the actuator simultaneously. The nonlinear plant is represented by the well‐known Takagi–Sugeno fuzzy model and the random data dropout is expressed by the Bernoulli random binary distribution. In the presence of random data dropout, two control schemes, state feedback and static output feedback, are proposed to design ??_∞ controllers such that the closed‐loop system is stochastically stable and preserves a guaranteed ??_∞ performance. The addressed controller design problem is transformed to an auxiliary convex optimization problem, which can be solved by a linear matrix inequality approach. Three examples are provided to illustrate the applicability and less conservativeness of the developed theoretical results. It is easy to see that our approach is simple but our results are much less conservative than the recently published results. Copyright © 2010 John Wiley & Sons, Ltd.     

Stabilization of positive coupled differential‐difference equations with unbounded time‐varying delays

This paper researches the static output‐feedback stabilization of single‐input single‐output (SISO) positive coupled differential‐difference equations (CDDEs) with unbounded time‐varying delays. First, a necessary and sufficient condition is provided for the positivity and asymptotical stability of CDDEs with unbounded time‐varying delays. For this type of system, based on the constructed estimates of its solution, a necessary and sufficient condition on asymptotical stability is provided. Then, based on this criterion, for CDDEs with unbounded time‐varying delays, a kind of static output‐feedback controller is designed to ensure the positivity and asymptotical stability of the corresponding closed‐loop systems. It is also worth pointing out that the controller is designed by the linear programming method without parameterization technique. This design approach can also be applied to the static state feedback stabilization problem of CDDEs with unbounded time‐varying delays. Finally, two illustrative examples are given to show the effectiveness of our results.     

Quadratic boundedness of LPV systems via saturated dynamic output feedback controller

For the linear parameter varying systems with bounded disturbance, a saturated dynamic output feedback controller is designed by specifically considering input saturation, to stabilize the closed‐loop system. The controller parameters and the corresponding region of attraction are calculated by solving an off‐line optimization problem with respect to input saturation, state constraints, and robust stability. In the off‐line optimization problem, both the unknown and available scheduling parameters are considered for the linear parameter varying systems. When the unknown scheduling parameters are considered, the off‐line optimization problem is nonconvex and can be solved by the cone complementary linearization method. When the available scheduling parameters are considered, the off‐line optimization problem can be reformulated as convex optimization due to the parameter dependent form of controller parameters. In the both cases, input saturation is specifically handled by introducing a set of linear matrix inequalities into the off‐line optimization problem, which can reduce the conservatism of the controller design and fully exploit the controller capability. Based on the real‐time estimated state, system output, and scheduling parameters, the actual input can be obtained by saturating the dynamic output feedback controller, and steer the augmented state quickly converge to the neighborhood of the origin. Two numerical examples are provided to illustrate the proposed approaches.     

Multiobjective fault‐tolerant fixed‐order/PID control of multivariable discrete‐time linear systems with unmeasured disturbances

In this paper, a multiobjective fault‐tolerant fixed‐order output feedback controller design technique is proposed for multivariable discrete‐time linear systems with unmeasured disturbances. Initially, a multiobjective fixed‐order controller is designed for the system by transforming the problem of tuning the parameters of the controller into a static output feedback problem and solving a mixed H₂/H_∞ optimization problem with bilinear matrix inequalities. Subsequently, the fixed‐order controller is used to construct the closed‐loop system and an active fault‐tolerant control scheme is applied using the input/output data collected from the controlled system. Motivated by its popularity in industry, the proposed method is also used to tune the parameters of proportional‐integral‐derivative controllers as a special case of structured controllers with the fixed order. Two numerical simulations are provided to demonstrate the design procedure and the flexibility of the proposed technique.     

Characterization and selection of global optimal output feedback gains for linear time‐invariant systems

The problem of global optimal static output feedback control for linear time‐invariant systems with linear quadratic index is investigated. The contributions of this paper are two‐fold. One is to investigate the dependence of the global optimal output feedback gain on the system initial conditions. The other is to construct a globally optimal feedback under a certain output measurement structure. Copyright © 2000 John Wiley & Sons, Ltd.     

Decentralized output‐feedback stabilization for interconnected discrete systems with unknown delays

The decentralized feedback stabilization problem of a class of nonlinear interconnected discrete‐time systems is considered. This class of systems has unknown‐but‐bounded state‐delay and uncertain nonlinear perturbations satisfying quadratic constraints that are functions of the overall state and delayed state vectors. A decentralized output feedback scheme is proposed and analyzed such that the overall closed‐loop system guarantees global delay‐dependent stability condition, derived in terms of local subsystem variables. Incorporating feedback gain perturbations, new resilient decentralized feedback scheme is subsequently developed. The proposed approach is formulated within the framework of convex optimization over linear matrix inequalities. Simulation results illustrate the effectiveness of the proposed decentralized output‐feedback controllers. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust H∞ control for uncertain linear neutral delay systems

This paper deals with the problem of robust H_∞ control for uncertain linear neutral delay systems. The parameter uncertainty under consideration is assumed to be norm‐bounded time‐invariant and appears in all the matrices of the state‐space model. The problem we address is the design of memoryless state feedback controllers such that the closed‐loop system is asymptotically stable and the H_∞ norm of the closed‐loop transfer function from disturbance to the controlled output is strictly less than a prescribed positive scalar for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the above problem is proposed. When this matrix inequality is feasible, an explicit expression for the desired state feedback controller is given. Furthermore, a numerical example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Design of simultaneous static output feedback low‐gain H∞ controllers for a collection of time‐delay system

This paper considers the design of simultaneous static output feedback controllers for a finite collection of time‐delay linear systems. By solving a minimization problem, we try to find an output feedback low‐gain controller such that all resultant closed‐loop time‐delay systems are internally stable and satisfy a prespecified H_∞‐norm requirement. Based on the barrier method, necessary conditions for local optimum of the minimization problem are derived. An example is given for illustration.     

Optimal regional pole placement for sun tracking control of high‐concentration photovoltaic (HCPV) systems: case study

This paper proposes an optimal regional pole placement approach for sun tracking control of high‐concentration photovoltaic systems. A static output feedback controller is designed to minimize an LQG cost function with a sector region pole constraint. The problem cannot be solved by LMI approach since it is a non‐convex optimization problem. Based on the barrier method, we instead solve an auxiliary minimization problem to obtain an approximate solution. Simulation results show the benefit of our approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Polynomial matrix solution of H2 optimal control problem for state‐space systems

A polynomial matrix solution to the H₂ output feedback optimal control problems is obtained for systems represented in state‐equation form. The proof does not invoke the separation principle but is obtained in the z‐domain. The cost function includes weighted states, which allows the so‐called standard system model problem to be solved. This encompasses the class of inferential control problems. The results also enable the two‐degree‐of‐freedom optimal control solution properties to be explored. Copyright © 2002 John Wiley & Sons, Ltd.     

Reduced‐order suboptimal control design for a class of nonlinear distributed parameter systems using POD and θ–D techniques

A new computational tool is presented in this paper for suboptimal control design of a class of nonlinear distributed parameter systems (DPSs). In this systematic methodology, first proper orthogonal decomposition‐based problem‐oriented basis functions are designed, which are then used in a Galerkin projection to come up with a low‐order lumped parameter approximation. This technique has evolved as a powerful model reduction technique for DPSs. Next, a suboptimal controller is designed using the emerging θ–D technique for lumped parameter systems. This time domain control solution is then mapped back to the distributed domain using the same basis functions, which essentially leads to a closed form solution for the controller in a state‐feedback form. We present this technique for the class of nonlinear DPSs that are affine in control. Numerical results for a benchmark problem as well as for a more challenging representative real‐life nonlinear temperature control problem indicate that the proposed method holds promise as a good optimal control design technique for the class of DPSs under consideration. Copyright © 2007 John Wiley & Sons, Ltd.     

Parametric uncertainty and disturbance attenuation in the suboptimal control of a non‐linear electrochemical process

The optimal control of the hydrogen evolution reactions is attempted for the regulation and change of set‐point problems, taking into account that model parameters are uncertain and I/O signals are corrupted by noise. Bilinear approximations are constructed, and their dimension eventually increased to meet accuracy requirements with respect to the trajectories of the original plant. The current approximate model is used to evaluate the optimal feedback through integration of the Hamiltonian equations. The initial value for the costate is found by solving a state‐dependent algebraic Riccati equation, and the resulting control is then suboptimal for the electrochemical process. The bilinear model allows for an optimal Kalman–Bucy filter application to reduce external noise. The filtered output is reprocessed through a non‐linear observer in order to obtain a state‐estimation as independent as possible from the bilinear model. Uncertainties on parameters are attenuated through an adaptive control strategy that exploits sensitivity functions in a novel fashion. The whole approach to this control problem can be applied to a fairly general class of non‐linear continuous systems subject to analogous stochastic perturbations. All calculations can be handled on‐line by standard ordinary differential equations integration software. Copyright © 2007 John Wiley & Sons, Ltd.     

A partitioning approach for H∞ control of singular time‐delay systems

This paper presents a new approach for delay‐dependent H_∞ stability analysis and control synthesis for singular systems with delay. By constructing an augmented Lyapunov–Krasovskii functional with a triple‐integral term, and using the partitioning technique, a bounded real lemma is presented to ensure the singular state‐delay system to be regular, impulse free and stable with γ‐disturbance rejection. The proposed result leads to significant performance improvement in system analysis and synthesis. Based on the criterion obtained, a homotopy‐based iterative LMI algorithm is developed to design a static output feedback controller. The feasibility and the effectiveness of theoretical developments are illustrated through numerical examples.Copyright © 2012 John Wiley & Sons, Ltd.     

Bilinear matrix inequality approaches to robust guaranteed cost control for uncertain discrete‐time delay system

The robust guaranteed cost control problem for uncertain discrete‐time delay system is considered in this paper. Sufficient conditions for the existence of the robust guaranteed cost controllers via memoryless state feedback and static output feedback are expressed as bilinear matrix inequality (BMI). Furthermore, the design methods of optimal robust guaranteed cost controllers, which minimize the upper bound of a given quadratic cost function are presented. Alternate iterative algorithms are proposed to solve the nonconvex optimization problems with BMI constrains. A numerical example is given to illustrate the effectiveness of the proposed methods.Copyright © 2012 John Wiley & Sons, Ltd.     

Robust preview control for uncertain discrete‐time systems based on LMI

For a class of uncertain discrete‐time systems, a preview controller based on linear matrix inequality is proposed. A new method is derived to construct an augmented error system instead of taking the difference of the error signal and the system equation. The new approach avoids applying the difference operator to the time‐varying matrix and can simplify the augmented error system. For the augmented error system of the uncertain system, state feedback is introduced. The sufficient condition of asymptotic stability of the closed‐loop system is derived for the performance index by using the relevant theorems of robust control theory. The condition can be realised by solving a linear matrix inequality optimization problem. By incorporating the controller obtained into the original system, we obtain the preview controller. Moreover, introducing an integrator allows the closed‐loop system to robustly track the desired tracking signal without steady‐state error.     

Distributed controller design and performance optimization for discrete‐time linear systems

This article addresses the problem of distributed controller design for linear discrete‐time systems. The problem is posed using the classical framework of state feedback gain optimization over an infinite‐horizon quadratic cost, with an additional sparsity constraint on the gain matrix to model the distributed nature of the controller. An equivalent formulation is derived that consists in the optimization of the steady‐state solution of a matrix difference equation, and two algorithms for distributed gain computation are proposed based on it. The first method consists in a step‐by‐step optimization of said difference matrix equation, and allows for fast computation of stabilizing state feedback gains. The second algorithm optimizes the same matrix equation over a finite time window to approximate asymptotic behavior and thus minimize the infinite‐horizon quadratic cost. To assess the performance of the proposed solutions, simulation results are presented for the problem of distributed control of a quadruple‐tank process, as well as a version of that problem scaled up to 40 interconnected tanks.