1,721,109 research outputs found
Probabilistic Analysis and Verification Framework for Adaptive Flight Control
Full text linkA crucial aspect that could facilitate the applications of adaptive control systems in aerospace applications is the development of effective validation and verification procedures. Most of the existing analysis and design frameworks for adaptive controllers are based on the Lyapunov direct method. One well-known drawback of this approach is the conservatism in the estimation of the uniform ultimate boundedness region with little practical utility. To overcome this limitation, a probabilistic framework for the design of uniform ultimate boundedness regions is proposed where uncertain parameters and adaptive controls are considered as random variables. In this framework, the design is translated into a stochastic convex optimization. This brings the benefit that (probabilistic) linear matrix inequality constraints can be derived without the need of matrix majorizations resulting therefore in less conservative conditions. Although the results are probabilistic, the level of confidence in the violation of linear matrix inequality constraints can be effectively established at the design level, exploiting the recent results of the probabilistic scenario design method. The approach is here applied for the design of uniform ultimate boundedness regions with prespecified component wise error requirements for a model reference adaptive control scheme in the presence of matched and input uncertainty. The approach is validated using the short-period longitudinal dynamics of an F-16 aircraft
Probabilistic Estimation of the Reachable Set of Model Reference Adaptive Controllers using the Scenario Approach
No full textA fundamental and critical problem for Model Reference Adaptive Control (MRAC) systems is the characterisation of the system response during transients. This problem is strictly related to the estimation of the reachable set (RS) from a fixed set of initial conditions and it is typically tackled using the Lyapunov\u27s direct method. One well-known drawback of this approach is the excessive conservatism in the estimation of the RS. To overcome this limitation the authors propose a novel probabilistic framework where uncertain parameters and control signals are considered as random variables. In this framework the RS design is translated into a stochastic convex optimisation problem. This brings the benefit that (probabilistic) LMIs with reduced conservatism can be worked out. The so-called scenario optimisation approach is then used to solve the stochastic optimisation problem with a-priori specified level of reliability. The novel approach is compared with an existing worst-case approach in determining the RS of MRAC systems in the presence of matched and input uncertainty via simulation studies. The proposed methodology can potentially be a useful tool for the probabilistic analysis and design of a broad category of existing adaptive control systems
A Non-Conservative Approach for the Estimation of the Region of Operation of Uncertain Adaptive Control Systems
No full textA challenging problem for Model Reference Adaptive Control Systems is the accurate characterization of the transient response in the presence of large uncertainties. Early prior research by the authors has demonstrated that using a projection mechanism for parameters adaptation the tracking error dynamics behaves as a linear system perturbed by bounded uncertainties. This brings the benefit that the stability analysis can be cast in terms of a convex optimization problem with LMI constraints so that efficient numerical tools can be used for the adaptive controller design. A possible limitation of the approach is that the design is restricted to quadratic control Lyapunov functions that could produce a conservative estimation of the regions of operation for the actual uncertain adaptive system. In this paper this approach is extended to arbitrary high degree polynomial Lyapunov functions by translating the design and performance requirements in terms of Sum of Square (SOS) inequalities and then using SOS optimization tools for the design. In this effort the new SOS approach is introduced and compared with the previous one. A numerical example based on the short period longitudinal dynamics of the F16 aircraft is used to demonstrate the efficacy of the novel method
Analysis and design of adaptive control systems with unmodeled input dynamics via multiobjective convex optimization
Full text linkA challenging problem for adaptive control systems is the accurate characterization of the transient response in the presence of dynamic uncertainties such as a partially known actuator. Considering an actuator modelled as a first order filter with an uncertain control effectiveness and using a projection mechanism for parameters adaptation, we show that the tracking error dynamics behaves as a linear system perturbed by bounded uncertainties. This brings the advantage that the stability analysis can be cast in terms of LMIs so that convex optimization tools can be used for analysis and design. In this framework we propose a mixed linear/adaptive control strategy whose parameters are computed via a convex Mult objective optimization in order to ensure, at the same time, the evolution of the error within a minimal size invariant set, while the added linear gain is minimized. A Numerical example is provided to demonstrate the efficacy of the method
A Model Reference Adaptive Control Approach for Uncertain Dynamical Systems with Strict Component-wise Performance Guarantees
No full textA critical problem for adaptive control systems is the characterization of the system re-sponse during transients. In fact a major issue in adaptive system design is the inability to achieve, a-priori, non-conservative user-defined performance guarantees. At present most of the available analysis tools provide performance bounds depending on the norm of uncertain quantities. Since it is extremely difficult to quantify these quantities, conservative upper bounds are used in their place; these, in turn, produce conservative performance bounds of limited practical utility. To face these problems some of the authors have recently introduced a set-theoretic adaptive controller based on generalized restricted potential functions. The key feature of this approach is that it allows the norm of the tracking error to be less than a-priori user-defined worst-case performance bound, and hence, it has the capability to enforce strict per-formance guarantees. Since this performance is expressed as function of the norm of the er-ror vector it is not possible to have the direct control on the amplitude of the single error components. In this paper the method is improved by allowing the control of the shape of the perfor-mance (ellipsoidal) set that is guaranteed to contain the tracking error trajectories. The de-sign problem is formalized as a linear optimization with LMI constraints that allows specify-ing independent componentwise requirements for the error components. Different linear optimization cost functions have been evaluated with the purpose of computing the largest ellipsoidal domain contained in an a-priori specified tracking error polyhedral domain and the smallest ellipsoidal domain containing an a-priori specified ellip-soidal initial condition set. A detailed simulation study in the aeronautic context has been used to highlight the efficacy of the method and the role of the different design parameters
Performance Oriented Adaptive Architectures with Guaranteed Bounds
Full text linkWhile adaptive control has been used in numerous applications to achieve given system stabilization or command following criteria, the ability to obtain a predictable transient performance is a challenging problem when there is no a priori knowledge about system uncertainties (e.g., their upper bounds and/or domains). In order to address this problem, a new method is presented in [1, 2] utilizing artificial basis functions in the update law of an adaptive control design. This approach is predicated on a gradient minimization procedure and achieves a predictable transient performance without inducing oscillations in the system response as the constant gain due to the nature of this minimization approach is judiciously increased. However, selection of this gain is problem dependent and may need to be adjusted for each different design. To address this problem, we present a new approach which has an ability to auto-tune an adaptive control design with artificial basis functions employed when the controlled system is about to violate a given design constraint on error dynamics (i.e., only when it is necessary). In particular, our approach is based on a controller architecture that allows the assignment of a priori known (user-defined) transient performance bounds. These bounds are constructed through a restricted potential function approach [3] that yields to an error dependent gain to adjust system performance for time instants when it is required to meet given design criteria. In addition to the theoretical results based on Lyapunov stability arguments highlighting transient performance of an uncertain system that stays within a priori given performance bounds, an illustrative example is provided to demonstrate the efficacy of the proposed framework
Model Reference Neuroadaptive Control Revisited: How to Keep the System Trajectories on a Given Compact Set
No full textSet Theoretic Performance Verification of Low-Frequency Learning Adaptive Controllers
No full textAlthough adaptive control has been used in numerous applications, the ability to obtain a predictable transient and steady-state closed-loop performance is still a challenging problem from the verification and validation standpoint. To that end, we considered a recently developed robust adaptive control methodology called low-frequency learning adaptive control and utilized a set of theoretic analysis to show that the transitory performance of this approach can be expressed, analyzed, and optimized via a convex optimization problem based on linear matrix inequalities. This key feature of this design and analysis framework allows one to tune the adaptive control parameters rigorously so that the tracking error components of the closed-loop nonlinear system evolve in a priori specified region of the state space whose size can be minimized by selecting a suitable cost function. Simulation examples are provided to demonstrate the efficacy of the proposed verification and validation architecture showing the possibility of performing parametric studies to analyze the interplay between the size of the tracking error residual set and important design parameters such as the adaptation rate and the low-pass filters time constant of the weights adaptation algorith
Adaptive Spacecraft Control: Stability, Performance, and Robustness
No full textThis paper designs a low-frequency learning adaptive control architecture for a flexible spacecraft. The proposed architecture involves a new and novel controller structure involving a modification term in the update law. In particular, this modification term filters out the high-frequency content contained in the update law while preserving stability of the system error dynamics. This key feature of our design allows for robust, fast adaptation in the face of high-gain learning rates. A numerical illustrative study is provided for a flexible spacecraft to demonstrate the efficacy of the proposed design
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