E. Dogan Sumer

Frequency-domain stability analysis of retrospective-cost adaptive control for systems with unknown nonminimum-phase zeros

We develop a multi-input, multi-output direct adaptive controller for discrete-time, possibly nonminimum-phase, systems with unknown nonminimum-phase zeros. The adaptive controller requires limited modeling information about the system, specifically, Markov parameters from the control input to the performance variables. Often, only a single Markov parameter is required, even in the nonminimum-phase case. We analysis the stability of the algorithm using a time-and-frequency-domain approach. We demonstrate the algorithm on disturbance-rejection problems, where the disturbance spectra are unknown. This controller is based on a retrospective performance objective, where the controller is updated using either batch or recursive least squares.

Retrospective Cost Adaptive Control for Systems with Unknown Nonminimum-Phase Zeros

We develop a multi-input, multi-output direct adaptive controller for discrete-time, possibly nonminimum-phase, systems with unknown nonminimum-phase zeros. The adaptive controller requires limited modeling information about the system, specifically, Markov parameters from the control input to the performance variables. Often, only a single Markov parameter is required, even in the nonminimum-phase case. We demonstrate the algorithm on command-following and disturbance-rejection problems, where the command and disturbance spectra are unknown. This controller is based on a retrospective performance objective, where the controller is updated using either batch or recursive least squares.

Robustness of retrospective cost adaptive control to Markov-parameter uncertainty

In this paper we investigate the robustness of an extended version of retrospective cost adaptive control (RCAC), in which less modeling information is required than in prior versions of this method. RCAC is applicable to MIMO possibly nonminimum-phase (NMP) plants without the need to know the locations of the NMP zeros. The only required modeling information is an FIR approximation of the plant, which may be based on a limited number of Markov parameters. In this paper we investigate the effect of phase mismatch between the true plant and the FIR approximation. Numerical examples demonstrate the relationship between phase mismatch at the command and disturbance frequencies as well as the required level of regularization in the controller update.

FIR-based phase matching for robust Retrospective-Cost Adaptive Control

In this paper we develop frequency-domain methods for approximating IIR plants with FIR transfer functions. The underlying goal is to increase the performance and robustness of Retrospective-Cost Adaptive Control (RCAC), which is applicable to MIMO possibly nonminimum-phase (NMP) plants without the need to know the locations of the NMP zeros. The only required modeling information is an FIR approximation of the plant, which may be based on a limited number of Markov parameters, or possibly noisy frequency response data. In this paper we investigate the resulting phase mismatch between the true plant and the FIR approximation obtained through linear and nonlinear approximation methods. We consider degradation in the phase mismatch due to uncertainty in the frequency response data.

Retrospective Cost Adaptive Control with Error-Dependent Regularization for MIMO Systems with Uncertain Nonminimum-Phase Transmission Zeros

In this paper we focus on retrospective cost adaptive control (RCAC), which is applicable to stabilization, command following, disturbance rejection, and model reference control problems for SISO and MIMO plants. RCAC uses limited modeling information, specifically, Markov parameters of the transfer function from the control input to the performance variable. Typically, a small number of Markov parameters are needed, for example, one Markov parameter usually suffices if the plant is minimum phase. If the plant is Lyapunov stable and nonminimum phase, then knowledge of the locations of the nonminimum-phase zeros is not needed as long as an error-dependent regularization term is used to weight the control effort. For plants that are both open-loop unstable and nonminimum phase, knowledge of the locations of the nonminimum-phase zeros may be needed. The goal of the present paper is to further investigate the effectiveness of the error-dependent regularization terms. Furthermore, we remove the intermediate step of reconstructing the retrospective controls and we directly update the controller. Next, we consider channelwise phase-matching conditions for MIMO plants. Finally, we investigate the role of zeros in MIMO nonsquare systems.

On the role of subspace zeros in retrospective cost adaptive control of non-square plants

We consider adaptive control of non-square plants, that is, plants that have an unequal number of inputs and outputs. In particular, we focus on retrospective cost adaptive control (RCAC), which is a direct, discrete-time adaptive control algorithm that is applicable to stabilisation, command following, disturbance rejection, and model reference control problems. Previous studies on RCAC have focused on control of square plants. In the square case, RCAC requires knowledge of the first non-zero Markov parameter and the non-minimum-phase (NMP) transmission zeros of the plant, if any. No additional information about the plant or the exogenous signals need be known. The goal of the present paper is to consider RCAC for non-square plants. Unlike the square case, we show that the assumption that the non-square plant is minimum phase does not guarantee closed-loop stability and signal boundedness. The main purpose of this paper is to establish the existence of time-invariant input and output subspaces corresponding to the adaptive controller. In particular, we show that RCAC implicitly squares down non-square plants through pre-/post-compensation of the non-square plant with a constant matrix. We show that, for wide plants, the control input generated by RCAC lies in a time-invariant ‘input subspace’, which is equivalent to pre-compensating the plant with a constant matrix. On the other hand, for tall plants, we show that the controller update is driven by the output of the plant post-compensated with a constant matrix. Accordingly, in either case, signal boundedness properties of the closed-loop system are determined by the transmission zeros of the squared system, which we call the ‘subspace zeros’. To deal with NMP subspace zeros, we introduce a robustness modification, which prevents RCAC from cancelling the NMP subspace zeros.

BROADBAND DISTURBANCE REJECTION USING RETROSPECTIVE COST ADAPTIVE CONTROL

We apply retrospective cost adaptive control (RCAC) to a broadband disturbance rejection problem under limited modeling information and assuming that the performance variable is measured. The goal is to compare the asymptotic performance (that is, after convergence of the controller) of the adaptive controller with the performance of discrete-time LQG controller, which uses complete modeling information but does not require a measurement of the performance variable. For RCAC we assume that the first nonzero Markov parameter of the plant is known. We show that if the plant zeros are also known, the retrospective cost can be modified to recover the high-control-authority LQG performance.Copyright

Adaptive decentralized noise and vibration control with conflicting performance objectives

Decentralized control is a longstanding challenge in systems theory. A decentralized controller may consist of multiple local controllers, connected to disjoint or overlapping sets of sensors and actuators, and where each local controller has limited ability to communicate directly with the remaining local controllers and, in addition, may lack global knowledge of the plant and operation of the remaining local controllers. In the present paper we apply adaptive control to investigate the ability of the local controllers to cooperate globally despite uncertainty, communication constraints, and possibly conflicting performance objectives. The approach we apply in this paper is based on retrospective cost adaptive control (RCAC). The development of RCAC assumes a centralized controller structure; the goal of the present paper is to investigate the stability and performance of RCAC in a decentralized setting.Copyright

Robust sampled-data adaptive control of the Rohrs counterexamples

We revisit the Rohrs counterexamples within the context of sampled-data adaptive control. In particular, retrospective cost adaptive control (RCAC) is applied to the sampled continuous-time plant with unmodeled high-frequency dynamics, which involves nonminimum-phase (NMP) sampling zeros. It is shown that, without knowledge of these NMP zeros, RCAC stabilizes the uncertain plant and asymptotically follows the sinusoidal command.

Adaptive control of uncertain Hammerstein systems with monotonic input nonlinearities using auxiliary nonlinearities

We extend retrospective cost adaptive control (RCAC) to command following for uncertain Hammerstein systems. We assume that only one Markov parameter of the linear plant is known and that the input nonlinearity is monotonic but otherwise unknown. Auxiliary nonlinearities are used within RCAC to account for the effect of the input nonlinearity.