Electrical and Electronic Engineering - Research Publications
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ItemExploiting homogeneity for the optimal control of discrete-time systems: Application to value iteration(IEEE, 2021)To investigate solutions of (near-)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discrete-time systems. Assuming the plant dynamics is homogeneous, we first derive a scaling property of its solutions along rays provided the sequence of inputs is suitably modified. We then consider homogeneous cost functions and reveal how the optimal value function scales along rays. This result can be used to construct (near-)optimal inputs on the whole state space by only solving the original problem on a given compact manifold of a smaller dimension. Compared to the related works of the literature, we impose no conditions on the homogeneity degrees. We demonstrate the strength of this new result by presenting a new approximate scheme for value iteration, which is one of the pillars of dynamic programming. The new algorithm provides guaranteed lower and upper estimates of the true value function at any iteration and has several appealing features in terms of reduced computation. A numerical case study is provided to illustrate the proposed algorithm.
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ItemObserving the Slow States of General Singularly Perturbed Systems(IEEE, 2020-01-01)This paper studies the behaviour of observers for the slow states of a general singularly perturbed system - that is a singularly perturbed system which has boundary-layer solutions that do not necessarily converge to a slow manifold. The solutions of the boundary-layer system are allowed to exhibit persistent (e.g. oscillatory) steady-state behaviour which are averaged to obtain the dynamics of the approximate slow system. It is shown that if an observer has certain properties such as asymptotic stability of its error dynamics on average, then it is practically asymptotically stable for the original singularly perturbed system.
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ItemAn Approach to Minimum Attention Control by Sparse Derivative(IEEE, 2020-01-01)Minimum attention control proposed by Brockett is an important formulation for resource-aware control, while his problem formulation and the underlying optimization problem that he proposed is in general very hard. In this paper, we propose a computationally tractable design method of minimum attention control based on promoting sparsity of the derivative of control. The optimal control problem is formulated as L0 norm minimization of the time derivative of control under the constraint that the derivative is bounded by a fixed value. This is a non-convex problem, and we propose L1 relaxation for linear systems to obtain optimal control by efficient numerical computation. We then show equivalence theorems between the L0 and L1 optimal controls. Also, we present an example of feedback control for the first-order integrator, that illustrates the proposed methodology.
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ItemSampled-data extremum-seeking control for optimization of constrained dynamical systems using barrier function methods(IEEE, 2020-03-12)Most extremum-seeking control approaches focus solely on the problem of finding the extremum of some unknown, steady-state performance map. However, many industrial applications also have to deal with constraints on operating conditions due to, e.g., actuator limitations, limitations on design or tunable system parameters, or constraints on measurable signals. These constraints, which can be unknown a-priori, may conflict with the otherwise optimal operational condition, and should be taken into account in performance optimization. In this work, we propose a sampled-data extremum-seeking approach for optimization of constrained dynamical systems using barrier function methods, where both the objective function and the constraint function are available through measurement only. We show that, under the assumption that initialization does not violate constraints, the interconnection between a constrained dynamical system and optimization algorithms that employ barrier function methods is stable, the constraints are satisfied, and optimization is achieved. We illustrate the results by means of a numerical example.
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ItemA unifying event-triggered control framework based on a hybrid small-gain theorem(IEEE, 2020-12-14)We propose a unifying emulation-based design framework for the event-triggered control of nonlinear systems that is based on a hybrid small-gain perspective. We show that various existing event-triggered controllers fit the unifying perspective. Moreover, we demonstrate that the flexibility offered by our approach can be used for the development of novel event-triggered schemes and for a systematic modification and improvement of existing schemes. Finally, we illustrate via a simulation example that these novel and/or modified event-triggered controllers can lead to a reduction in the required number of transmissions, while still guaranteeing the same stability properties.
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ItemStochastic stabilisation and power control for nonlinear feedback loops communicating over lossy wireless networks(IEEE, 2020-01-01)We study emulation-based stabilisation of nonlinear networked control systems communicating over multiple wireless channels subject to packet loss. Specifically, we establish sufficient conditions on the rate of transmission that guarantee Lp stability-in-expectation of the overall closed-loop system. These conditions depend on the cumulative dropout probability of the network nodes for static protocols. We use the obtained stability results to study power control, where we show there are interesting trade-offs between the transmission rate, transmit power, and stability. Lastly, numerical examples are presented to illustrate our results.
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ItemState estimation of non-linear systems over random access wireless networks(IEEE, 2021-01-01)We study emulation-based state estimation for non-linear plants that communicate with a remote observer over a shared wireless network subject to packet losses. To reduce bandwidth usage, a stochastic communication protocol is employed to determine which node should be given access to the network. We describe the overall wireless system as a hybrid model, which allows us to capture the behaviour both between and at transmission instants, whilst covering network features such as random transmission instants, packet losses, and stochastic scheduling. Under this setting, we provide sufficient conditions on the transmission rate that guarantee an input-to-state stability property for the corresponding estimation error system. We illustrate our results with an example of Lipschitz non-linear plants.
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ItemEvent-triggered observer design for linear systems(IEEE, 2021-01-01)We present an event-triggered observer design for linear time-invariant systems, where the measured output is sent to the observer only when a triggering condition is satisfied. We proceed by emulation and we first construct a continuous-time Luenberger observer. We then propose a dynamic rule to trigger transmissions, which only depends on the plant output and an auxiliary scalar state variable. The overall system is modeled as a hybrid system, for which a jump corresponds to an output transmission. We show that the proposed event-triggered observer guarantees global practical asymptotic stability for the estimation error dynamics. Moreover, under mild boundedness conditions on the plant state and its input, we prove that there exists a uniform strictly positive minimum inter-event time between any two consecutive transmissions, guaranteeing that the system does not exhibit Zeno solutions. Finally, the proposed approach is applied to a numerical case study of a lithium-ion battery.
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ItemJoint Parameter and State Estimation of Noisy Discrete-Time Nonlinear Systems: A Supervisory Multi-Observer Approach(IEEE, 2021-01-01)This paper presents two schemes to jointly estimate parameters and states of discrete-time nonlinear systems in the presence of bounded disturbances and noise. The parameters are assumed to belong to a known compact set. Both schemes are based on sampling the parameter space and designing a state observer for each sample. A supervisor selects one of these observers at each time instant to produce the parameter and state estimates. In the first scheme, the parameter and state estimates are guaranteed to converge within a certain margin of their true values in finite time, assuming that a sufficiently large number of observers is used and a persistence of excitation condition is satisfied in addition to other observer design conditions. This convergence margin is constituted by a part that can be chosen arbitrarily small by the user and a part that is determined by the noise levels. The second scheme exploits the convergence properties of the parameter estimate to perform subsequent zoom-ins on the parameter subspace to achieve stricter margins for a given number of observers. The strengths of both schemes are demonstrated using a numerical example.
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