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Register a new userOptimal control of nonlinear systems with unsymmetrical input constraints and its applications to the UAV circumnavigation problem
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In this paper, a new design scheme is presented to solve the optimal control problem for nonlinear systems with unsymmetrical input constraints. This method also relaxes the assumption in the current study for the adaptive optimal control, that is, the internal dynamics should hold zero when the state of the system is in the origin. Particularity, the partially-unknown system is investigated and the procedure to obtain the corresponding optimal control policy is introduced. The optimality of the obtained control policy and the stability for the closed-loop dynamics are proved theoretically. Meanwhile, the proposed method in this paper can be further applied to nonlinear control systems whose dynamics are completely known or unknown. Besides, we apply the control design framework proposed in this paper to solve the optimal circumnavigation problem involving a moving target for a fixed-wing unmanned aerial vehicle (UAV). The control performance of our method is compared with that of the existing circumnavigation control law in a numerical simulation and the simulation results validate the effectiveness of our algorithm.
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This paper presents a constrained deep adaptive dynamic programming (CDADP) algorithm to solve general nonlinear optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state constraints. Both the policy and value function are approximated by deep neural networks (NNs), which directly map the system state to action and value function respectively without needing to use hand-crafted basis function. The proposed algorithm considers the state constraints by transforming the policy improvement process to a constrained optimization problem. Meanwhile, a trust region constraint is added to prevent excessive policy update. We first linearize this constrained optimization problem locally into a quadratically-constrained quadratic programming problem, and then obtain the optimal update of policy network parameters by solving its dual problem. We also propose a series of recovery rules to update the policy in case the primal problem is infeasible. In addition, parallel learners are employed to explore different state spaces and then stabilize and accelerate the learning speed. The vehicle control problem in path-tracking task is used to demonstrate the effectiveness of this proposed method.
We address the problem of designing simultaneous input and state interval observers for Lipschitz continuous nonlinear systems with rank-deficient feedthrough, unknown inputs and bounded noise signals. Benefiting from the existence of nonlinear decomposition functions and affine abstractions, our proposed observer recursively computes the maximal and minimal elements of the estimate intervals that are proven to contain the true states and unknown inputs. Moreover, we provide necessary and sufficient conditions for the existence and sufficient conditions for the stability (i.e., uniform boundedness of the sequence of estimate interval widths) of the designed observer, and show that the input interval estimates are tight, given the state intervals and decomposition functions.
A simultaneous input and state interval observer is presented for Lipschitz continuous nonlinear systems with unknown inputs and bounded noise signals for the case when the direct feedthrough matrix has full column rank. The observer leverages the existence of bounding decomposition functions for mixed monotone mappings to recursively compute the maximal and minimal elements of the estimate intervals that are compatible with output/measurement signals, and are proven to contain the true state and unknown input. Furthermore, we derive a Lipschitz-like property for decomposition functions, which provides several sufficient conditions for stability of the designed observer and boundedness of the sequence of estimate interval widths. Finally, the effectiveness of our approach is demonstrated using an illustrative example.
One of the most important branches of nonlinear control theory is the so-called sliding-mode. Its aim is the design of a (nonlinear) feedback law that brings and maintains the state trajectory of a dynamic system on a given sliding surface. Here, dynamics becomes completely independent of the model parameters and can be tuned accordingly to the desired target. In this paper we study this problem when the feedback law is subject to strong structural constraints. In particular, we assume that the control input may take values only over two bounded and disjoint sets. Such sets could be also non perfectly known a priori. An example is a control input allowed to switch only between two values. Under these peculiarities, we derive the necessary and sufficient conditions that guarantee sliding-mode control effectiveness for a class of time-varying continuous-time linear systems that includes all the stationary state-space linear models. Our analysis covers several scientific fields. It is only apparently confined to the linear setting and allows also to study an important set of nonlinear models. We describe fundamental examples related to epidemiology where the control input is the level of contact rate among people and the sliding surface permits to control the number of infected. For popular epidemiological models we prove the global convergence of control schemes based on the introduction of severe restrictions, like lockdowns, to contain epidemic. This greatly generalizes previous results obtained in the literature by casting them within a general sliding-mode theory.
We address the problem of robust state reconstruction for discrete-time nonlinear systems when the actuators and sensors are injected with (potentially unbounded) attack signals. Exploiting redundancy in sensors and actuators and using a bank of unknown input observers (UIOs), we propose an observer-based estimator capable of providing asymptotic estimates of the system state and attack signals under the condition that the numbers of sensors and actuators under attack are sufficiently small. Using the proposed estimator, we provide methods for isolating the compromised actuators and sensors. Numerical examples are provided to demonstrate the effectiveness of our methods.
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