The (multi-player) linear quadratic state feedback control problem for index one descriptor systems

In this paper, we propose a new approach for a robust multirate lane-keeping control scheme with predictive virtual lanes. First, the multirate lane-keeping control scheme is proposed to improve the lane-keeping performance and to reduce the ripple in the yaw rate. To improve the lane-keeping performance on a curved road, the integral of the lateral offset error is added to the state feedback controller. A multirate Kalman filter (KF) has been developed to resolve the problems caused by slow lane detection due to the vision processing system. This multirate KF estimates vehicle states at a fast rate using a microprocessor. Utilizing the estimated states, the linear quadratic state feedback control operates at the same fast update rate of the microprocessor. Thus, a multirate control scheme can reduce the ripple in the yaw rate. Second, we propose a virtual lane prediction method that compensates for the momentary failure of lane detection from unexpected problems. If the camera sensor momentarily fails while obtaining lane information, the predicted virtual lane can be substituted for the lane detection using the camera sensor in the proposed control scheme. Thus, the proposed control scheme can normally operate when the lane information is momentarily unavailable. The performance of the proposed method was evaluated via experiments.

The stabilization problem of linear time-varying uncertain delay systems by means of linear constant memoryless state feedback control is investigated here. In the case when uncertain parameters may vary independently in arbitrarily large bounding sets, the locations of uncertain elements in the system parameters play an important role. So far obtained conditions of this problem have been found to have a particular geometric configuration with respect to the permissible locations of uncertain elements. In this paper, such a previously obtained configuration is developed to a basic form of antisymmetric stepwise configuration which is a necessary and sufficient condition for time-varying uncertain systems without delays to be quadratically stabilizable by means of linear constant state feedback control. It is shown that if a given system satisfies such developed conditions then the system is stabilizable via linear constant state feedback control with regardless to the upper bounds of time-varying uncertain parameters and time-varying delays

This paper concerns the problems of robust stability analysis and stabilization for uncertain linear system with time-varying delay. In order to obtain a robust stability criterion with less conservative for uncertain linear delay system, a quadratic integral inequality is improved by matrix decomposition. Further, two different kinds of controller, i.e., linear memoryless state feedback controller and linear state feedback controller with state delay, are derived in terms of the robust stability criteria. Two numeral examples are provided to demonstrate the validity of the proposed methods.

This paper studies the discrete-time indefinite stochastic linear quadratic optimal control problem with the equality terminal state constraints,which can be transformed into a mathematical programming with equality constraints. By means of matrix Lagrange theorem, a necessary condition for the existence of optimal linear state feedback control is given. The previous results on discrete-time stochastic linear quadratic optimal control without constraints, can be viewed as corollaries of the main theorem of this paper.

ABSTRACTThe regional robust stabilisation by means of linear time-invariant state feedback control for a class of uncertain MIMO nonlinear systems with parametric uncertainties and control input saturation is investigated. The nonlinear systems are described in a differential algebraic representation and the regional stability is handled considering the largest ellipsoidal domain-of-attraction (DOA) inside a given polytopic region in the state space. A novel set of sufficient Linear Matrix Inequality (LMI) conditions with new auxiliary decision variables are developed aiming to design less conservative linear state feedback controllers with corresponding larger DOAs, by considering the polytopic description of the saturated inputs. A few examples are presented showing favourable comparisons with recently published similar control design methodologies.

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.

This paper discusses a systematic control design for a three-phase L-filtered grid-connected inverter using linear matrix inequality-based optimization method. A state feedback control is employed to provide stability to the inverter system and with the inclusion of integral control the offset error can be eliminated. In addition, the proposed control is implemented in dq-synchronous frame with help from a phase locked-loop to track the grid phase angle. The optimization criterion of this proposed control is to reduce the convergence time to the steady state as short as possible. The set of robust stabilizing gain is systematically discussed in this paper and computed using MATLAB toolbox. Then, the effectiveness of this proposed control algorithm is verified by implementing on PSIM simulation tool.

Decentralized Output Feedback Control of Interconnected Uncertain Delay Systems

A global sliding mode controller (GSMC) is proposed for the missile electromechanical actuator (EA) servo system, where exists high uncertainties, such as parameter variations and external disturbances. By the design of an optimal integral switching function based on optimal linear quadratic regulator (LQR) theory, the initial state of system is set on the switching surface, and the optimal sliding mode motion is produced. The proposed GSMC is composed of an optimal linear state feedback controller (OLSFC), and a fuzzy nonlinear robust controller (FNRC), which can be designed respectively. The OLSFC, generated by the designed switching function, intends to minimise a quadratic performance index, and then improves the dynamic performance of system. Meanwhile, the FNRC employs a fuzzy decision maker (FDM), which estimates the upper bound of uncertainties as FNRC’s gain adaptively, and then makes GSMC robust and control input smooth. With the computer simulations on an EA experiment plant, it presents that the proposed scheme possesses good tracking precision, effective suppression against chattering at control input, and strong robustness against system uncertainties.

This paper designs a discrete-time state-feedback output tracking control for the heart rate during treadmill exercise. Initially, the nonlinear model describing the relationship between the heart rate and the speed of a treadmill is discretized. Afterwards, a feedback linearization-based control law is proposed to achieve perfect output tracking. The control objective is to make the runner's heart rate follow a heart rate reference profile set by especialists as reference. The set-up of the problem in discrete time allows taking into consideration the effect of sampling during the controller design procedure instead of relegating it to the implementation stage. It will be shown that a linear state feedback controller is enough to make the nonlinear model's output track the reference profile regardless its possibly complex time variation. Since the full state is not available for measurement a reduced order state observer is incorporated into the discrete-time control law. Then, the continuous control command is generated by using a zero order hold (ZOH). The designed control system is tested on the original continuous-time nonlinear model by computer simulation to demonstrate the effectiveness of the proposed method to achieve the required objective.

This paper presents a novel observer-based controller design method for discrete-time piecewise affine (PWA) systems. The basic idea is as follows: at first, a piecewise linear (without affine terms) state feedback controller and a PWA observer are designed separately, and then it is proved that the output feedback controller constructed by the resulting observer and state feedback controller gains can guarantee the stability of the closed-loop system. During the controller design, the piecewise-quadratic Lyapunov function technique is used. Moreover, the region information is taken into account to treat the affine terms, so the controller gains can be obtained by solving a set of linear matrix inequalities, which are numerically feasible with commercially available software. Three simulation examples are given finally to verify the proposed theoretical results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Stability Analysis and Control of Bilinear Discrete-Time Systems: A Dual Approach

The designs of two linear control systems approach to stabilize the balance of an unmanned bicycle system are presented. Both approaches are based on the use of a reaction wheel or flywheel to balance the bicycle. The two linear control approaches, based on the linearization of a nonlinear model obtained using Lagrange formalism, are the classic linear controllers, PID and State Feedback control. The performance of both controllers is verified by digital simulation and real-time experimental results.

Perturbation estimation based robust state feedback control for grid connected DFIG wind energy conversion system

In this paper a new linear state feedback controller for artificial pancreas is proposed to regulate the blood glucose level in diabetic patients. Diabetes mellitus is a family of chronic metabolic diseases in which body's blood glucose regulatory system doesn't function properly. In this study, Bergman's minimal model has been used as a base model, to reformulate dynamics of insulin and glucose concentrations in blood's plasma as a constrained polynomial dynamical system. Since it is hard to derive exact value of parameters in most biological systems, all parameters of the model has been considered uncertain and therefore parametric uncertainty has been exploited in control design. Based on sum of squares technique, a linear state feedback controller has been obtained to regulate the blood's insulin and glucose concentration levels around the basal levels. Main achievements of this paper are simplicity of controller structure which makes it easy to implement, parametric uncertainty to cover more patients and patient-nonspecific design, and employment of nonlinear techniques without any simplifications.