1,721,037 research outputs found
A Performance Analysis of Two Approximate Adaptive Designs
No full textThe performance of function approximator based adaptive control designs may scale badly with approximator dimension [1]. For a simple system class, both projection based designs and multi-resolution approximation based designs have been shown to have good scaling properties w.r.t. to LQ costs. Here we show that by considering a cost functional with penalties on the control rate, the multi-resolution approximator based design can outperform the projection based design. Generalisations are briefly discussed
Gap Metric Robustness of Adaptive Controllers
No full textWe consider the construction of adaptive controllers for minimum phase linear systems which achieve non-zero robustness margins in the sense of the (linear) L2(0,∞) gap metric. The gap perturbations may be more constrained for larger disturbances and for larger parametric uncertainty. Working within the framework of the nonlinear gap metric [3], universal adaptive controllers are first given achieving this goal for first order plants, and the results are then generalised to relative degree one, minimum phase plants
Robust Stability of Iterative Learning Control Schemes
No full textA notion of robust stability is developed for iterative learning control in the context of disturbance attenuation. The size of the unmodelled dynamics is captured via a gap distance, which in turn is related to the standard H2 gap metric, and the resulting robustness certificate is qualitatively equivalent to that obtained in classical robust H∞ theory. A bound on the robust stability margin for a specific adaptive ILC design is established
Gap metric robustness of a backstepping control design
No full textA robust backstepping controller is designed for a plant in strict-feedback form which is perturbed by both input and measurement disturbances. The closed-loop is shown to be gain-function stable, and stable under Lipschitz conditions on the nonlinearities. This controller is also shown to achieve stability for any perturbed plant whose gap distance from the strict-feedback system is less than some computable quantity
A performance comparison of robust adaptive controllers: linear systems
No full textWe consider robust adaptive control designs for relative degree one, minimum phase linear systems of known high frequency gain. The designs are based on the dead-zone and projection modifications, and we compare their performance w.r.t. a worst case transient cost functional with a penalty on the L∞ norm of the output, control and control derivative. We establish two qualitative results. If a bound on the L∞ norm of the disturbance is known and the known a priori bound on the uncertainty level is sufficiently conservative, then it is shown that a dead-zone controller outperforms a projection controller. The complementary result shows that the projection controller is superior to the dead-zone controller when the a priori information on the disturbance level is sufficiently conservative
Robust stability for multiple model adaptive control: part II - gain bounds
Full text linkThe axiomatic development of a wide class of Estimation based Multiple Model Switched Adaptive Control (EMMSAC) algorithms considered in the first part of this two part contribution forms the basis for the proof of the gain bounds given in this paper. The bounds are determined in terms of a cover of the uncertainty set, and in particular, in many instances, are independent of the number of candidate plant models under consideration.The full interpretation, implications and usage of these bounds within design synthesis are discussed in part I. Here in part II, key features of the bounds are also discussed and a simulation example is considered. It is shown that a dynamic EMMSAC design can be universal and hence non-conservative and hence outperforms static EMMSAC and other conservative designs. A wide range of possible dynamic algorithms are outlined, motivated by both performance and implementation considerations
Graph Topologies, Gap Metrics and Robust Stability for Nonlinear Systems
No full textGraph topologies for nonlinear operators which admit coprime factorisations are defined w.r.t. a gain function notion of stability in a general normed signal space setting. Several metrics are also defined and their relationship to the graph topologies are examined. In particular relationships between nonlinear generalisations of the gap and graph metrics, Georgiou-type formulae and the graph topologies are established. Closed loop robustness results are given w.r.t. the graph topology, where the role of a coercivity condition on the nominal plant is emphasised
Efficient minimal disturbance estimation in estimation based multiple model switched adaptive control
No full textThis paper addresses the problem of efficiently solving the minimal disturbance estimation problems in Estimation based Multiple Model Switched Adaptive Control (EMMSAC) for a large set of linear time-invariant candidate plant models. We show that it is possible to approximate the minimal disturbance measure functional of any member in the original set by only using the minimal disturbance measure functionals for a basic candidate plant models set chosen from the original set via a bank of low-pass, high-pass, and band-pass filters. We also analyse the efficiency of the proposed method
Robust stability for multiple model adaptive control: part I - the framework
Full text linkAn axiomatic framework providing robust stability and performance bounds for a wide class of Estimation based Multiple Model Switched Adaptive Control (EMMSAC) algorithms is developed. The approach decouples development of both the atomic control designs and the estimation processes thus permitting the usage of standard controller design and optimisation approaches for these components. The framework is shown to give tractable algorithms for MIMO LTI plants, and also for some classes of nonlinear systems (for example, an integrator with input saturation). The gain bounds obtained have the key feature that they are functions of the complexity of the underlying uncertainty as described by metric entropy measures. For certain important geometries, such as a compact parametric uncertainties, the gain bounds are independent of the number of plant models (above a certain threshold) which are utilized in the implementation. Design processes are described for achieving a suitable sampling of the plant uncertainty set to create a finite candidate plant model set (whose size is also determined by a metric entropy measure) which achieves a guaranteed robustness/performance
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