Alessandro Pisano

Robust boundary control of a diffusion process with spatially varying, unknown diffusivity, matched additive disturbance, and an uncertain, time-varying input gain is addressed. An adaptive sliding-mode boundary controller is proposed, combining a proportional and discontinuous term whose gain updates monotonically via a gradient-based adaptation law. No a priori bounds on the disturbances are required for tuning. Under standard boundedness and positivity assumptions for the uncertain drift disturbance and control gains, global asymptotic stability of the closed-loop origin in the L₂-sense is established via a tailored Lyapunov construction and Barbalat’s lemma. Numerical simulations verify and illustrate the theoretical findings.

A sliding mode–based adaptive control law is proposed for a class of diffusion processes featuring a spatially‐varying uncertain diffusivity and equipped with several point‐wise actuators located at the two boundaries of the spatial domain as well as in its interior. The system is additionally perturbed by matched disturbances which are assumed to be uniformly bounded along with their time derivatives. The corresponding constant bounds are unknown , thus motivating the use of an adaptive control strategy. To achieve global asymptotic stability of the origin in the ‐sense, a control law consisting of a proportional and discontinuous term is proposed. The gain of the discontinuous term is continuously adjusted according to a gradient‐based adaptation algorithm. The stability and convergence analysis is Lyapunov‐based and it constructively yields simple tuning conditions for the controller gain parameters. Simulation results are finally discussed to support the theoretical findings.

Dynamic boundary control design is addressed for an uncertain heat process in order to regulate its state to a constant set-point value while also rejecting a smooth unmatched boundary disturbance. The diffusivity parameter is unknown a priori, and a control signal is applied to the plant at its boundary through a first-order dynamic actuation with uncertain time constant, thereby yielding a coupled PDE/ODE representation of the overall system dynamics. The proposed output feedback design is sliding mode based, and it is made under collocated sensing. Its Lyapunov stability analysis is developed in the Sobolev state space $H^{2}(0,1)$ to additionally conclude the uniform pointwise-in-space exponential stabilization of the closed-loop error dynamics. Numerical simulations are involved to corroborate the theoretical findings.

A sliding-mode-based adaptive boundary control law is proposed for a class of uncertain thermal reaction-diffusion processes subject to matched disturbances. The disturbances are assumed to be bounded, but the corresponding bounds are unknown, thus motivating the use of adaptive control strategies. A boundary control law comprising a proportional and discontinuous term is proposed, wherein the magnitude of the discontinuous relay term is adjusted via a gradient-based adaptation algorithm. Depending on how the adaptation algorithm is parameterized, the adaptive gain can be either a nondecreasing function of time (monodirectional adaptation) or it can both increase and decrease (bidirectional adaptation). The convergence and stability properties of these two solutions are investigated by Lyapunov analyses, and two distinct stability results are derived, namely, asymptotic stability for the monodirectional adaptation and globally uniformly ultimately bounded solutions for the bidirectional adaptation. The proposed algorithms are then specified to address the control problem of stabilizing a desired temperature profile in a metal beam equipped with thermoelectric boundary actuators. Experiments are conducted to investigate the real-world performance of the proposed sliding-mode-based adaptive control, with a particular focus on comparing the monodirectional and bidirectional adaptation laws.

Summary: This paper proposes a sliding‐mode‐based adaptive boundary control law for stabilizing a class of uncertain diffusion processes affected by a matched disturbance. The matched disturbance is assumed to be uniformly bounded along with its time derivative, whereas the corresponding upper bounding constants are not known. This motivates the use of adaptive control strategies. In addition, the spatially‐varying diffusion coefficient is also uncertain. To achieve asymptotic stability of the plant origin in the ‐sense in the presence of the disturbance, a discontinuous boundary feedback law is proposed where the gain of the discontinuous control term is adjusted according to a gradient‐based adaptation law. A constructive Lyapunov analysis supports the stability properties of the considered closed‐loop system, yielding sufficient convergence conditions in terms of suitable inequalities involving the controllers' tuning parameters. Simulation results are presented to corroborate the theoretical findings.

This article addresses the state estimation and unknown input reconstruction in strongly observable linear systems under the so-called matching conditions. Our proposal extends previous approaches to predefined-time state estimation, which involved the use of a pair of time-delay observers, adapting them to the framework of sliding-mode observation in the presence of unknown inputs. As a result, a novel sliding-mode-based observation algorithm is developed, which exhibits desirable properties, such as global finite-time convergence or semiglobal fixed-time convergence. Notably, the method is also capable of reconstructing the unknown inputs without requiring any low-pass filtering or continuous approximations of the discontinuous observer signals. The convergence properties are proven through a formal stability analysis and validated through numerical simulations.

For uncertain linear system subjected to uniformly bounded unknown inputs it is presented a novel finite-time unknown input first-order sliding-mode observer. The strategy involves the design of a pair of quadratically stable first-order sliding-mode observers, aimed to guarantee the robustness to non-smooth unknown inputs and the finite-time convergence to zero of the output estimation errors. Then, the exact estimation of the unmeasured states is achieved in a fixed-time since the sliding motion is established through the design of an auxiliary output consisting of a delayed linear-combination of the estimations provided by the above-mentioned pair of observers. To confirm the effectiveness of the proposed scheme, along with a sketch of the proof of its convergence characteristics, a detailed numerical comparison analysis with the existing first-order sliding-mode competitor observers is illustrated.

This present article addresses the feedback control design problem of in-line liquid flow heating units used to process silicon wafers in the semiconductor industry. A physics-based model is developed to describe the thermal behavior of the heater and the liquid circulating in it. Under sensible approximations, process dynamics are shown to be governed by a coupled partial differential equation (PDE)/ordinary differential equation (ODE) system. A boundary control law capable of steering the fluid temperature to the desired set-point value while rejecting matched disturbances is developed. The proposed boundary control is sliding-mode-based and makes use of boundary measurements only. The convergence properties of the closed-loop system are formally demonstrated by means of Lyapunov-based analysis. In addition, the input-to-state stability (ISS) properties of the closed-loop system with respect to nonmatching boundary disturbances are investigated. To corroborate the theoretical findings, this article additionally presents the experimental results with the proposed controller implemented in the closed loop on a real in-line heating unit.