Athanasios Sideris

H ∞ control with parametric Lyapunov functions

A new control synthesis approach is proposed for linear parametrically varying (LPV) systems using parameter-dependent quadratic Lyapunov functions. The synthesis problem is formulated via a set of linear matrix inequalities (LMIs). When solved, parameter-dependent controllers are obtained that stabilize the LPV systems and achieve guaranteed performance in an L2-gain sense. The new approach includes the case of parameter-independent Lyapunov functions, and as a result provides additional flexibility in the control design.

H/sub /spl infin// optimization with time-domain constraints

Standard H/sub /spl infin// optimization cannot handle specifications or constraints on the time response of a closed-loop system exactly. In this paper, the problem of H/sub /spl infin// optimization subject to time-domain constraints over a finite horizon is considered. More specifically, given a set of fixed inputs w/sup i/, it is required to find a controller such that a closed-loop transfer matrix has an H/sub /spl infin//-norm less than one, and the time responses y/sup i/ to the signals w/sup i/ belong to some prespecified sets /spl Omega//sup i/. First, the one-block constrained H/sub /spl infin// optimal control problem is reduced to a finite dimensional, convex minimization problem and a standard H/sub /spl infin// optimization problem. Then, the general four-block H/sub /spl infin// optimal control problem is solved by reduction to the one-block case. The objective function is constructed via state-space methods, and some properties of H/sub /spl infin// optimal constrained controllers are given. It is shown how satisfaction of the constraints over a finite horizon can imply good behavior overall. An efficient computational procedure based on the ellipsoid algorithm is also discussed. >

High bandwidth tilt measurement using low-cost sensors

A state estimation technique is developed for sensing inclination angles using relatively low cost sensors. A low bandwidth tilt sensor is used along with an inaccurate rate gyro to obtain the measurement. The rate gyro has an inherent bias along with sensor noise. The tilt sensor uses an internal pendulum and therefore has its own slow dynamics. These sensor dynamics were identified experimentally and combined to achieve high bandwidth measurements using an optimal linear state estimator. Potential uses of the measurement technique range from robotics, to rehabilitation, to vehicle control.

Elimination of frequency search from robustness tests

An example is given which demonstrates that the multivariable stability margin can be a discontinuous function of frequency. A method which checks for robustness without a frequency search and thus alleviates the associated difficulties is proposed. It is shown that robustness can be verified by solving only one multivariable stability margin problem, readily constructed from a state-space realization of the given plant. >

Single-input-single-output H ∞ control with time domain constraints

Standard H∞ optimization cannot handle specifications or constraints on the time response of a closed loop system exactly. In this paper the problem of H∞ optimization subject to time domain constraints over a finite horizon is considered. Following an idea from Helton and Sideris (1989, IEEE Trans. Aut. Control, AC-34, 427–434) the problem is transformed into a finite dimensional optimization program that is shown to be convex although generically nondifferentiable. The objective function is constructed via state space methods and several properties of the optimal constrained controller are discussed together with a robust algorithm for computation. It is shown how satisfying the constraints over a finite horizon can imply overall good behavior.

An efficient sequential linear quadratic algorithm for solving nonlinear optimal control problems

We develop a numerically efficient algorithm for computing controls for nonlinear systems that minimize a quadratic performance measure. We formulate the optimal control problem in discrete-time, but many continuous-time problems can be also solved after discretization. Our approach is similar to sequential quadratic programming for finite-dimensional optimization problems in that we solve the nonlinear optimal control problem using sequence of linear quadratic subproblems. Each subproblem is solved efficiently using the Riccati difference equation. We show that each iteration produces a descent direction for the performance measure, and that the sequence of controls converges to a solution that satisfies the well-known necessary conditions for the optimal control.

Recent Advances on the Algorithmic Optimization of Robot Motion

An important technique for computing motions for robot systems is to conduct a numerical search for a trajectory that minimizes a physical criteria like energy, control effort, jerk, or time. In this paper, we provide example solutions of these types of optimal control problems, and develop a framework to solve these problems reliably. Our approach uses an efficient solver for both inverse and forward dynamics along with the sensitivity of these quantities used to compute gradients, and a reliable optimal control solver. We give an overview of our algorithms for these elements in this paper. The optimal control solver has been the primary focus of our recent work. This algorithm creates optimal motions in a numerically stable and efficient manner. Similar to sequential quadratic programming for solving finite-dimensional optimization problems, our approach solves the infinite-dimensional problem using a sequence of linear-quadratic optimal control subproblems. Each subproblem is solved efficiently and reliably using the Riccati differential equation.

Propellant Injector Influence on Liquid-Propellant Rocket Engine Instability

The avoidance of acoustic instabilities, which may cause catastrophic failure, is demanded for liquid-propellant rocket engines. This occurs when the energy released by combustion amplifies acoustic disturbances; it is therefore essential to avoid such positive feedback. Although the energy addition mechanism operates in the combustion chamber, the propellant injector system may also have considerable influence on the stability characteristics of the overall system, with pressure disturbances in the combustion chamber propagating back and forth in the propellant injectorchannels.Theintroducedtimedelaymayaffectstability,dependingontheratioofthewavepropagationtime throughtheinjectortotheperiodofthecombustionchambersacousticmodes.Thisstudyfocusesontransverse-wave liquid-propellant rocket engine instabilities using a two-dimensional polar coordinate solver (with averaging in the axial direction) coupled to one-dimensional solutions in each of the coaxial oxygen–methane injectors. A blockage in one (or more) of the injectors is analyzed as a stochastic event that may cause an instability. A properly designed temporaryblockage of oneor more injectors can also be used for control of an oscillation introduced by any physical event.Thestochasticanddesignvariablesparameterspaceis exploredwiththepolynomial chaosexpansionmethod.

H ∞ -control with time domain constraints: the infinite horizon case

Abstract It has been shown recently that time domain constraints can be incorporated into H ∞ - optimal control problems when the constraints are enforced over a finite horizon, i.e. over a finite number of sample instants. This is done in (Sideris and Rotstein, 1993; Rotstein and Sideris, to appear) where the finite horizon problem is reduced into a finite dimensional, convex, but generically nondifferentiable optimization program. In this paper, the infinite horizon case is addressed. It is shown that when the horizon length goes to infinity, the solutions to the finite horizon problems converge to a solution of the infinite horizon problem. Moreover, a simple modification of the finite horizon problems guarantees convergence to a solution that is easily approximated by a finite dimensional transfer function.

A Riccati approach for constrained linear quadratic optimal control

An active-set method is proposed for solving linear quadratic optimal control problems subject to general linear inequality path constraints including mixed state-control and state-only constraints. A Riccati-based approach is developed for efficiently solving the equality constrained optimal control subproblems generated during the procedure. The solution of each subproblem requires computations that scale linearly with the horizon length. The algorithm is illustrated with numerical examples.