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Register a new userDual-control based approach to batch process operation under uncertainty based on optimality-conditions parameterization
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This paper presents a scheme for dual robust control of batch processes under parametric uncertainty. The dual-control paradigm arises in the context of adaptive control. A trade-off should be decided between the control actions that (robustly) optimize the plant performance and between those that excite the plant such that unknown plant model parameters can be learned precisely enough to increase the robust performance of the plant. Some recently proposed approaches can be used to tackle this problem, however, this will be done at the price of conservativeness or significant computational burden. In order to increase computational efficiency, we propose a scheme that uses parameterized conditions of optimality in the adaptive predictive-control fashion. The dual features of the controller are incorporated through scenario-based (multi-stage) approach, which allows for modeling of the adaptive robust decision problem and for projecting this decision into predictions of the controller. The proposed approach is illustrated on a case study from batch membrane filtration.
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In this paper, we propose a new control barrier function based quadratic program for general nonlinear control-affine systems, which, without any assumptions other than those taken in the original program, simultaneously guarantees forward invariance of the safety set, complete elimination of undesired equilibrium points inside it, and local asymptotic stability of the origin. To better appreciate this result, we first characterize the equilibrium points of the closed-loop system with the original quadratic program formulation. We then provide analytical results on how a certain parameter in the original quadratic program should be chosen to remove the undesired equilibrium points or to confine them in a small neighborhood of the origin. The new formulation then follows from these analytical results. Numerical examples are given alongside the theoretical discussions.
In this paper a novel approach to co-design controller and attack detector for nonlinear cyber-physical systems affected by false data injection (FDI) attack is proposed. We augment the model predictive controller with an additional constraint requiring the future---in some steps ahead---trajectory of the system to remain in some time-invariant neighborhood of a properly designed reference trajectory. At any sampling time, we compare the real-time trajectory of the system with the designed reference trajectory, and construct a residual. The residual is then used in a nonparametric cumulative sum (CUSUM) anomaly detector to uncover FDI attacks on input and measurement channels. The effectiveness of the proposed approach is tested with a nonlinear model regarding level control of coupled tanks.
A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled, the proposed method aims at propagating uncertainties effectively and optimizing control parameters to satisfy the probabilistic requirements directly. To achieve this, the sensitivities of violation probabilities are evaluated by the expansion coefficients and the fourth moment method for reliability analysis, after which an optimization that minimizes failure probability under chance constraints is conducted. Afterward, a time-dependent polynomial chaos expansion is performed to validate the results. With this approach, the failure probability is reduced while guaranteeing the closed-loop performance, thus increasing the safety margin. Simulations are carried out on a longitudinal model subject to uncertain parameters to demonstrate the effectiveness of this approach.
In the interaction between control and mathematics, mathematical tools are fundamental for all the control methods, but it is unclear how control impacts mathematics. This is the first part of our paper that attempts to give an answer with focus on solving linear algebraic equations (LAEs) from the perspective of systems and control, where it mainly introduces the controllability-based design results. By proposing an iterative method that integrates a learning control mechanism, a class of tracking problems for iterative learning control (ILC) is explored for the problem solving of LAEs. A trackability property of ILC is newly developed, by which analysis and synthesis results are established to disclose the equivalence between the solvability of LAEs and the controllability of discrete control systems. Hence, LAEs can be solved by equivalently achieving the perfect tracking tasks of resulting ILC systems via the classic state feedback-based design and analysis methods. It is shown that the solutions for any solvable LAE can all be calculated with different selections of the initial input. Moreover, the presented ILC method is applicable to determining all the least squares solutions of any unsolvable LAE. In particular, a deadbeat design is incorporated to ILC such that the solving of LAEs can be completed within finite iteration steps. The trackability property is also generalized to conventional two-dimensional ILC systems, which creates feedback-based methods, instead of the common used contraction mapping-based methods, for the design and convergence analysis of ILC.
We pose the aggregators problem as a bilevel model, where the upper level minimizes the total operation costs of the fleet of EVs, while each lower level minimizes the energy available to each vehicle for transportation given a certain charging plan. Thanks to the totally unimodular character of the constraint matrix in the lower-level problems, the model can be mathematically recast as a computationally efficient mixed-integer program that delivers charging schedules that are robust against the uncertain availability of the EVs. Finally, we use synthetic data from the National Household Travel Survey 2017 to analyze the behavior of the EV aggregator from both economic and technical viewpoints and compare it with the results from a deterministic approach.
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