Admissibility-Preserving Control for Strict-Feedback Nonlinear Systems with Asymmetric Actuator Constraints

Saurabh Kumar; Shashi Ranjan Kumar; Abhinav Sinha

eess.SYAug 15, 2026

Admissibility-Preserving Control for Strict-Feedback Nonlinear Systems with Asymmetric Actuator Constraints

Authors: Saurabh Kumar, Shashi Ranjan Kumar, Abhinav Sinha

Organizations: Intelligent Systems and Control (ISaC) Lab, Department of Aerospace Engineering, Indian Institute of Technology Bombay, Maharashtra 400076 India · Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, OH 45221, USA

Abstract

This paper develops Admissibility-Preserving Control (APC), a realization-centered safety-critical control framework for strict-feedback systems subject to asymmetric actuator limits, time-varying output constraints, and actuator-rate limitations. APC denotes the overall control architecture, whereas an Admissibility-Preserving Input Realization (APIR) denotes its constraint-realization module. Therein, the APIR dynamically generates the physical plant input while rendering its prescribed asymmetric actuator set forward invariant. In contrast to algebraic clipping and post-design saturation compensation, the actuator limits are embedded directly in a continuously differentiable dynamic realization with user-selectable regularity and interpretable tuning parameters. The APIR is integrated with recursive backstepping by treating the realized plant input as an additional state. The resulting design does not require an input-to-state stability assumption on the uncontrolled plant. Instead, the nonlinear drift terms are compensated recursively, subject to an explicit compatibility condition between the desired motion, the available control authority, and the APIR interior gain. The framework is further extended to time-varying output-safe tracking through a smooth asymmetric logarithmic barrier coordinate and its associated Lyapunov function and to simultaneous actuator-magnitude and rate constraints through a cascaded APIR. Rigorous Lyapunov and invariance analyses establish regional asymptotic tracking, forward invariance of the compatible admissible sets, and boundedness of all closed-loop signals. Numerical studies illustrate asymmetric actuator utilization, output-safety preservation, and magnitude-rate constraint enforcement.

Figures & tables

Panel of Figure 1 — Fig. 1 : Canonical APC architecture. The control-synthesis layer generates $u_{c}$ , while the APIR dynamically realizes the physical plant input $u\in\mathbb{U}$ .

Panel of Figure 2 — Fig. 2 : Parametric response of the asymmetric APIR ( 3 ) to the constant command $u_{c}=15$ with $u_{\max}=10$ and $u_{\min}=-7$ .

Scenario	Case labels	Initial plant states $\left(x_{1}(0),x_{2}(0)\right)$
Asymmetric magnitude constraint	$C_{1}$ , $C_{2}$ , $C_{3}$	$(0,0)$ , $(-0.2,0.25)$ , $(0.6,-0.1)$
Time-varying output-safe tracking	$I_{1}$ , $I_{2}$ , $I_{3}$	$(0.1,0.538)$ , $(0.25,0.174)$ , $(0.4,-0.156)$
Constant output-safe tracking	$S_{1}$ , $S_{2}$	$(0.1,0.509)$ , $(0.35,-0.03)$
Magnitude–rate constraints	$R_{1}$ , $R_{2}$ , $R_{3}$	$(0.05,0.6)$ , $(0.2,0.296)$ , $(0.35,-0.012)$

TABLE I : Simulation cases and initial conditions.

Panel of Figure 4 — Fig. 3 : Output tracking with bounded input.

Panel of Figure 5 — Fig. 4 : Constrained (time-varying) output tracking with bounded input.

Panel of Figure 6 — Fig. 5 : Constrained (constant) output tracking with bounded input.

Panel of Figure 7 — Fig. 6 : Output tracking with bounded input and rate.

Panel of Figure 8 — Fig. 7 : APC gain conditioning.

Panel of Figure 9 — Fig. 8 : APC baseline comparison.

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Admissibility-Preserving Control for Multi-Input Systems with Joint Capacity Constraints

Saurabh Kumar, Lohitvel Gopikannan, Shashi Ranjan Kumar, Abhinav Sinha

Intelligent Systems & Control (ISaC) Lab, Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India · Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering, University of Cincinnati, OH 45221, USA

Backstepping Control Feedback Control

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This paper addresses the control of multi-input strict-feedback nonlinear systems subject to a joint capacity constraint, in which the admissible input set is a coupled subset of the individual actuator limits. Unlike existing constraint-handling methods that enforce actuator bounds channel by channel and may unnecessarily suppress admissible control directions, we develop an Anisotropic Joint-Admissibility-Preserving Input Realization (AJ-APIR) framework that explicitly exploits the geometry of the joint constraint. The proposed realization constructs a state-dependent gain matrix whose spectral decomposition separates the commanded input into normal and tangential directions relative to the constraint boundary. The normal component is attenuated as the boundary is approached, while the tangential component is preserved, which allows the admissible control effort to be redistributed without loss of tracking authority. Integrated with a backstepping controller, the AJ-APIR framework guarantees forward invariance of the joint admissible set for all time. We establish exponential convergence of the tracking error to zero together with uniform boundedness of all closed-loop signals, and characterize the resulting command-demand behavior under the joint constraint. Simulation results for a representative second-order, two-input nonlinear system subject to a power-budget constraint demonstrate the efficacy of the proposed method to enforce the joint input constraint.

Abstract

Backstepping Control

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