Structured State Space Uncertainty Research Articles

Model‐based event‐triggered control of singularly perturbed system with dual event‐triggering mechanism

AbstractIn this article, a new dual event‐triggering mechanism is proposed to implement a distributed model‐based event‐triggered control for a singularly perturbed system (SPS) having structured state space uncertainty. The proposed approach significantly reduces the amount of necessary information exchanged to control the system. Dual event‐triggering mechanism allows the measurements of slow and fast states to be transmitted asynchronously at different rates which is more effective due to the two time‐scale nature of SPSs. Approximate slow and fast systems of the nominal plant are used as the model to reduce the computational demand. The proposed control strategy guarantees that the system states converge to an adjustable region around the equilibrium point and the inter‐event intervals are lower‐bounded by a positive constant. A numerical simulation example is used to illustrate the theoretical results of the article.

Robust eigenstructure assignment for the extended medium range air-to-air missile

A new sufficient condition for the robust stability of a linear time invariant system subject to linear time varying structured state space uncertainty is presented. This sufficient condition is a sum of terms each of which involves the ith right eigenvector, the ith left eigenvector, and the real part of the ith eigenvalue. This new robustness result is less conservative than an earlier result which involves the modal matrix and the real part of the eigenvalue which is closest to the imaginary axis in the complex plane. A robust design is computed for the Extended Medium Range Air-to-Air Missile and the new design is compared with an earlier orthogonal projection eigenstructure assignment design. The new design method uses the MATLAB TM Optimization Toolbox to minimize the integral of the deviations of the integrated roll rate (which is approximately the bank angle) from zero. The integral is approximated by a sum of discrete samples of the integrated roll rate while normalizing the integration width to unity. Constraints are placed on the real part of the Dutch roll and roll mode eigenvalues, the damping ratios of the Dutch roll and roll mode, the aileron and rudder deflection rates, and the sufficient condition for robust stability. The new design satisfies the robustness condition while also yielding an improved transient response.

Minimum-effort interception of multiple targets

References ^heres, E., Gutman, S., and Palmor, Z. J., of Uncertain Dynamic Systems Including State Delay, IEEE Transactions on Automatic 'Control Vol. 34, No. 11, 1989, pp. 1199-1203. Thorp, J. S., and Barmish, B. R., On Quarantee Stability of Ultimate Linear Systems via Linear Journal of Optimization Theory and Applications, Vol. 35, No. 4, 1981, pp. 559-579. Tsay, S. C., Fong, I. K., and Kuo, T. S., Linear Quadratic Optimal Control for Systems with Linear Uncertainties, International} ournal of Control, Vol. 53, No. 1, 1991, pp. 81-96. Schmitendorf, W. E., Designing Stabilizing Controllers for Uncertain Systems Using the Riccati Equation Approach, IEEE Transactions on Automatic Control, Vol. 33, No. 4, 1988, pp. 376-379. Zhou, K., and Khargonekar, P. P., Stabilization of Linear Systems with Norm-Bounded Time-Varying Uncertainty, Systems and Control Letters, Vol. 10, No. 1, 1988, pp. 17-20. Mcruer, D. T., and Bates, C. L., Dynamics of the Airframe, Navy Bureau Aeronaut. Rept. AE-61-411, 1952. Sobel, K. M., Banda, S. S., and Yeh, H. H., Control for Linear Systems with Structured State Space Uncertainty, InternationalJournal of Control, Vol. 50, No. 5, 1989, pp. 1991-2004. Jabbari, F., and Schmitendorf, W. E., A Noniterative Method for the Design of Linear Robust Controllers, IEEE Transactions on Automatic Control, Vol. 35, No. 8, 1990, pp. 954-957. Petersen, I. R., and Hollot, C. V., A Riccati Equation Approach to the Stabilization of Uncertain Linear Systems, Automatica, Vol. 22, No. 4, 1986, pp. 397-411.

Robust eigenstructure assignment with structured state space uncertainty

Recent sufficient conditions for robust stability and robust performance of linear time-invariant systems subject to structured state-space uncertainty are utilized to obtain a robust eigenstructure assignment design method. This new approach optimizes either the sufficient condition for stability or performance robustness while constraining the dominant eigenvalues to lie within chosen regions in the complex plane. This constrained optimization problem is solved by using the sequential unconstrained minimization technique with a quadratic extended interior penalty function. The use of constraints on certain eigenvector entries and the effect of these constraints on robustness and nominal performance are considered. Conservatism of the robustness conditions is reduced by simultaneously introducing a similarity transformation, a positive real diagonal weighting, and a unitary weighting into the design procedure. An example that illustrates the design of a robust eigenstructure assignment controller for a pitch pointing/vertical translation maneuver of the AFTIF-16 aircraft is presented.

Robust control for linear systems with structured state space uncertainty

Abstract A recent sufficient condition for the stability robustness of linear systems with time-varying norm bounded state space uncertainty is extended to include the structure of the uncertainty. Our new result requires that the nominal eigenvalues lie to the left of a vertical line in the complex plane which is determined by a norm involving the structure of the uncertainty and the nominal closed-loop eigenvector matrix. Therefore, this robustness result is especially well suited to the design of control systems using eigenstructure assignment. When the uncertainty is time-invariant, our norm is also an upper bound on the incremental eigenvalue perturbations. We also consider the use of Perron weightings to reduce conservatism and the extension of the results to discrete time systems.