T. Runolfsson

Vibrational feedback control: Zeros placement capabilities

It is shown that in addition to closed-loop pole placement, vibrational feedback controllers lead, in the sense specified below, to a possibility of open-loop zeros assignability. On this basis, the superior performance characteristics of continuous-time periodic controllers, discovered in [3]-[6], are explained.

Residence time control

The problem of residence time controllability in dynamical systems with stochastic perturbations is formulated. The solution is given for linear systems with small, additive, white-noise perturbation. It is shown that the existence of the desired residence time controller depends on the relationship between the column spaces of the control and noise matrices. If the former includes the latter, any residence time is possible. If this inclusion does not occur, the achievable residence time is bounded: lower and upper estimates of this bound are given. For each of these cases, controller-design techniques are suggested and illustrative examples are considered. The development is based on an asymptotic version of the large deviations theory. >

Output residence time control

The problem of residence time control is extended to systems with outputs. Necessary and sufficient conditions for output residence time controllability in linear systems with small amounts of additive noise are derived. Design techniques for state-feedback controllers are developed and applied to a robotics control problem. The approach is based on an extension of the asymptotic first passage time theory to output processes. >

Residence probability control

Abstract The problem of controlling the residence probability of linear stochastic systems in a bounded domain is considered. Necessary and sufficient conditions for the existence of a controller that makes the residence probability positive (weakly residence probability controllable systems) and arbitrarily close to one (strongly residence probability controllable systems) are derived. The approach is based on the modern large deviations theory for systems perturbed by small white noise.

Output aiming control

The problem of aiming control, introduced in [1], is extended to systems with outputs. Necessary and sufficient conditions for output residence time controllability in linear SISO systems with small, additive noise are derived. Controller design techniques are developed and applied to aircraft and robotics control problems. The approach is based on an extension of the asymptotic first passage time theory to output processes.

Linear periodic feedback: Zeros placement capabilities

It is shown that in addition to closed loop pole placement, linear periodic controllers lead, in the sense specified below, to a possibility of open loop zeros assignability. On this basis, the superior performance characteristics of periodic controllers, discovered in [3]-[7], are explained.

Residence time control of systems subject to measurement noise

The residence time control problem is considered for linear systems that are subject to both input and measurement noise disturbances. It is shown that the maximal residence time is bounded, and an upper bound is derived. Necessary and sufficient conditions for the existence of controllers that achieve the upper bound are derived and design techniques for residence time controllers are considered. Connections with optimal output feedback control are explored. It is concluded that even if a system is strongly residence time-controllable, i.e. any residence time is achievable by a state feedback control law, any amount of measurement noise will result in a bounded residence time. Therefore, measurement noise has greater limiting effect than input noise on the achievable residence time.<<ETX>>

Vibrational Feedback Control

Abstract It is shown that in addition to closed loop pole placement, vibrational feedback controllers lead, in the sense specified below, to a possibility of open loop zeros assignability. On this basis, the superior performance characteristics of continuous time periodic controllers, discovered in [5]-[8], are explained. Furthermore, we show that periodic controllers have additional advantages in the strong and simultaneous stabilization problems.

On residence probability control

The problem of controlling the residence probability of a linear stochastic system in a bounded domain is considered. Necessary and sufficient conditions for the existence of a controller that makes the residence probability positive (weakly residence-probability-controllable systems) and arbitrarily close to one (strongly residence-probability-controllable systems) are derived. The approach is based on the modern large-deviations theory for systems perturbed by small white noise. It is concluded that system is weakly residence-probability-controllable if and only if it is stabilizable (in a certain sense) on the interval (0, T), and it is strongly residence-probability-controllable if and only if the image of the noise input matrix is contained in the image of the control input matrix.<<ETX>>

Aiming control: design of residence probability controllers

Methods for the design of residence probability (RP) controllers for linear stochastic systems are developed. Comparisons with H/sub 2/- and H/sub infinity /-optimal designs are given. In particular, it is shown that in the so-called strong RP-controllability case, every RP-optimal controller is H/sub 2/- and H/sub infinity /-optimal; the converse is not true. In the weak RP-controllability case, the H/sub infinity /-optimal controllers result in RP arbitrarily close to 0. The design of gains for RP-controllers is not more complex than that in the linear quadratic Gaussian (LQG) method: it only involves solving a Riccati equation. However, unlike the LQG, RP-controllers require the selection of the initial set D/sub 0/ as well; this is accomplished by solving a Lyapunov equation.<<ETX>>