Advantages of Fuzzy Control While Dealing with Complex/ Unknown Model Dynamics: A Quadcopter Example

Commonly, complex and uncertain plants cannot be faced through well-known linear approaches. Most of the time, complex controllers are needed to attain expected stability and robustness; however, they usually lack a simple design methodology and their actual implementation is difficult (if not impossible). Fuzzy logic control is an intelligent technique which, on its basis, allows the translation from logic statements to a nonlinear mapping. Although it has been proven to effectively deal with complex plants, many recent studies have moved away from the basic premise of linguistic interpretability. In this work, a simple fuzzy controller is designed in a clear way, privileging design easiness and logical consistency of linguistic operators. It is simulated together to a nonlinear model of a quadcopter with added actuators variability, so the robust operation of the controller is also proven. Uneven gain, bandwidth, and time-delay variations are applied among quadcopter’s motors, so the simulations results enclose those characteristics which could be found in reality. As those variations can be related to actuators’ performance, an analysis can be driven in terms of the features which are not commonly included in mathematical models like power electronics drives or electric machinery. These considerations may shorten the gap between simulation and actual implementation of the fuzzy controller. Briefly, this chapter presents a simple fuzzy controller which deals with a quadcopter plant as a first approach to intelligent control

オペレータリロンニモトヅクアツデンアクチュエータヲモチイタヘイバンコウゾウブツノヒセンケイシンドウセイギョニカンスルケンキュウ

博士（学術）東京農工大

Nonlinear robust H∞ control.

A new theory is proposed for the full-information finite and infinite horizontime robust H∞ control that is equivalently effective for the regulation and/or tracking problems of the general class of time-varying nonlinear systems under the presence of exogenous disturbance inputs. The theory employs the sequence of linear-quadratic and time-varying approximations, that were recently introduced in the optimal control framework, to transform the nonlinear H∞ control problem into a sequence of linearquadratic robust H∞ control problems by using well-known results from the existing Riccati-based theory of the maturing classical linear robust control. The proposed method, as in the optimal control case, requires solving an approximating sequence of Riccati equations (ASRE), to find linear time-varying feedback controllers for such disturbed nonlinear systems while employing classical methods. Under very mild conditions of local Lipschitz continuity, these iterative sequences of solutions are known to converge to the unique viscosity solution of the Hamilton-lacobi-Bellman partial differential equation of the original nonlinear optimal control problem in the weak form (Cimen, 2003); and should hold for the robust control problems herein. The theory is analytically illustrated by directly applying it to some sophisticated nonlinear dynamical models of practical real-world applications. Under a r -iteration sense, such a theory gives the control engineer and designer more transparent control requirements to be incorporated a priori to fine-tune between robustness and optimality needs. It is believed, however, that the automatic state-regulation robust ASRE feedback control systems and techniques provided in this thesis yield very effective control actions in theory, in view of its computational simplicity and its validation by means of classical numerical techniques, and can straightforwardly be implemented in practice as the feedback controller is constrained to be linear with respect to its inputs

International Conference on Dynamic Control and Optimization - DCO 2021: book of abstracts

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Theory of nonlinear feedback under uncertainty

AbstractOur main purpose here is to demonstrate the potential of a new approach which is an important expansion of the feedback concept: we have chosen what seemed a natural way of tackling some traditional problems of the control theory and of comparing the results against those offered by conventional methods.The main problem considered is the output stabilization for uncertain plants. Using structural transformations, uncertain systems can change to the form convenient for output feedback design. Synthesis of observer-based control for asymptotical stabilization or uniform ultimate boundedness of the closed-loop system is provided.We consider the notions of asymptotic and exponential invariance of a control system implies its suboptimality.A method is described for stabilization of uncertain discrete-time plants of which only compact sets are known to which plants parameters and exogenous signals belong. New approaches for solving some central problems of mathematical control theory are considered for nonlinear dynamical systems. New criterious of local and global controllability and stabilizability are indicated and some synthesis procedures are suggested

Aeronautical engineering: A continuing bibliography with indexes (supplement 275)

This bibliography lists 379 reports, articles, and other documents introduced into the NASA scientific and technical information system in Jan. 1991