Linear Quadratic State Feedback Control Research Articles

Robust Multirate Control Scheme With Predictive Virtual Lanes for Lane-Keeping System of Autonomous Highway Driving

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.

Optimal decentralized state-feedback control with sparsity and delays

This work presents the solution to a class of decentralized linear quadratic state-feedback control problems, in which the plant and controller must satisfy the same combination of delay and sparsity constraints. Using a novel decomposition of the noise history, the control problem is split into independent subproblems that are solved using dynamic programming. The approach presented herein both unifies and generalizes many existing results.

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

This paper gives a complete characterization of all optimal linear quadratic static state feedback controllers if the system is described by an index one descriptor system E x ˙ ( t ) = Ax ( t ) + Bu ( t ) . No definiteness restrictions are made with respect to the quadratic performance criterion. The explicit characterization of all solutions is achieved by transforming to a coordinate system, which can be computed by performing a singular value decomposition of E. This enhances the formulation of a numerical algorithm to calculate the solutions. Based on this explicit characterization of the solution set, we can characterize the set of all linear feedback Nash equilibria, in the context of non-cooperative linear quadratic differential games. The results are illustrated in an example.

Optimal control of precision paraboloidal shell structronic systems

Paraboloidal shells of revolution are commonly used in advanced aerospace, civil and telecommunication structures, e.g., antennas, reflectors, mirrors, rocket fairings, nozzles, solar collectors, dome structures, etc. A structronic shell system is defined as an elastic shell embedded, bonded or laminated with distributed piezoelectric sensors and actuators and it is governed by either in situ or external control electronics. A closed-loop control system of paraboloidal shell structronic system consists of distributed sensors/actuators and controller coupled with an elastic paraboloidal shell. State equation for the paraboloidal shell structronic system is derived and optimal linear quadratic state feedback control is implemented, such that the “best” shell control performance with the least control cost can be achieved. The gain matrix is estimated based on minimizing a performance criterion function. Optimal control effects are compared with controlled responses with other non-optimal control parameters. Control effects of identical-sized sensor/actuator patches at different locations are studied and compared. Modal control effects for different natural modes are also investigated.

Reliable linear-quadratic state-feedback control

This paper introduces a procedure for the design of modified linear-quadratic (LQ) state-feedback controls that tolerate actuator outages. The controls improve on the known stability gain-margin properties of the standard LQ regulator by tolerating the insertion of any independent gains from zero to infinity into selected feedback loops. They also guarantee a given performance bound despite the insertion of gains from zero to two into those loops. The reliable LQ design is shown to be equivalent to a standard LQ-optimal design with a modified performance index. Thus, the design procedure is seen as a means of choosing a particular quadratic performance index for which the optimal control will possess the desired reliability properties.

Output feedback controllers of suboptimality degree beta

A misconception in a recent paper by D.Z. Zheng (1989) about suboptimal feedback control is highlighted. A novel synthesis method for designing output feedback controllers of suboptimality degree beta is developed. These controllers yield a cost value equal to or less than a scalar multiple ( beta ) times the cost value obtained by optimal linear quadratic state feedback control. The output feedback control gains are explicit in terms of the standard Riccati equation when certain conditions are satisfied. >