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Controlling the behaviors of large language models (LLM) is fundamental to their safety alignment and reliable deployment. However, existing steering methods are primarily driven by empirical insights and lack theoretical performance…
The numerical reconstruction of controls for nonlinear partial differential equations (PDEs) remains a challenging and relatively underdeveloped problem, despite the extensive literature on controllability theory. In this work, we introduce…
This paper presents a safe delay-adaptive control for a strict-feedback nonlinear ODE with a delayed actuator, whose dynamic is also a strict-feedback nonlinear ODE and the delay length is unknown. By formulating the delay as a transport…
Adaptive stepsize control is a critical feature for the robust and efficient numerical solution of initial-value problems in ordinary differential equations. In this paper, we show that adaptive stepsize control can be incorporated within a…
Nonlinear PID control systems for a quadrotor UAV are proposed to follow an attitude tracking command and a position tracking command. The control systems are developed directly on the special Euclidean group to avoid singularities of…
Learning to perform perfect tracking tasks based on measurement data is desirable in the controller design of systems operating repetitively. This motivates the present paper to seek an optimization-based design approach for iterative…
This paper is concerned with the regulation control of a one-dimensional reaction-diffusion equation in the presence of a state-delay in the reaction term. The objective is to achieve the PI regulation of the right Dirichlet trace with a…
This article establishes the foundation for a new theory of invariant/integral manifolds for non-autonomous dynamical systems. Current rigorous support for dimensional reduction modelling of slow-fast systems is limited by the rare events…
Since the classical proportional-integral-derivative (PID) controller has continued to be the most widely used feedback methods in engineering systems by far, it is crucial to investigate the working mechanism of PID in dealing with…
In this paper, we adopt results in nonlinear time series analysis for causal inference in dynamical settings.~Our motivation is policy analysis with panel data, particularly through the use of "synthetic control" methods. These methods…
We consider an 1D partial integro-differential equation (PIDE) comprising of an 1D parabolic partial differential equation (PDE) and a nonlocal integral term. The control input is applied on one of the boundaries of the PIDE. Partitioning…
We present a data-driven nonlinear predictive control approach for the class of discrete-time multi-input multi-output feedback linearizable nonlinear systems. The scheme uses a non-parametric predictive model based only on input and noisy…
Direct torque control is considered as one of the most efficient techniques for speed and/or position tracking control of induction motor drives. However, this control scheme has several drawbacks: the switching frequency may exceed the…
Many engineered as well as naturally occurring dynamical systems do not have an accurate mathematical model to describe their dynamic behavior. However, in many applications, it is possible to probe the system with external inputs and…
Optimal tracking of continuous time nonlinear systems has been extensively studied in literature. However, in several applications, absence of knowledge about system dynamics poses a severe challenge to solving the optimal tracking problem.…
In this paper, an offset-free bilinear model predictive control approach for wind turbines is presented. State-of-the-art controllers employ different control loops for pitch angle and generator torque which switch depending on wind…
This paper concerns the adaptive control of a class of discrete-time nonlinear systems with all states accessible. Recently, a high-order tuner algorithm was developed for the minimization of convex loss functions with time-varying…
We consider a robust stabilization of the fourth-order oscillatory systems with non-collocated output sensing. Worth recalling is that the fourth-order systems are relatively common in mechatronics as soon as there are two-mass or more…
We consider the design of a new class of passive iFIR controllers given by the parallel action of an integrator and a finite impulse response filter. iFIRs are more expressive than PID controllers but retain their features and simplicity.…
The response to a setpoint change in PID controlled feedback systems plays an important role for the tuning methods. This response may be easily evaluated in linear systems without delay by solving the related ordinary differential…