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
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
Fig. 1 : Canonical APC architecture. The control-synthesis layer generates uc , while the APIR dynamically realizes the physical plant input u∈U .
Fig. 2 : Parametric response of the asymmetric APIR ( 3 ) to the constant command uc=15 with umax=10 and umin=−7 .
Scenario
Case labels
Initial plant states (x1(0),x2(0))
Asymmetric magnitude constraint
C1 , C2 , C3
(0,0) , (−0.2,0.25) , (0.6,−0.1)
Time-varying output-safe tracking
I1 , I2 , I3
(0.1,0.538) , (0.25,0.174) , (0.4,−0.156)
Constant output-safe tracking
S1 , S2
(0.1,0.509) , (0.35,−0.03)
Magnitude–rate constraints
R1 , R2 , R3
(0.05,0.6) , (0.2,0.296) , (0.35,−0.012)
TABLE I : Simulation cases and initial conditions.
Fig. 3 : Output tracking with bounded input.
Fig. 4 : Constrained (time-varying) output tracking with bounded input.
Fig. 5 : Constrained (constant) output tracking with bounded input.
Fig. 6 : Output tracking with bounded input and rate.
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.
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
This paper addresses safety-critical coordination for scalar agents whose distributed commands are implemented through constrained physical-input dynamics. Agents communicate over a fixed weighted digraph with a directed spanning tree, while their outputs must remain inside a common moving safety corridor and their realized inputs must satisfy heterogeneous asymmetric bounds. We propose a networked Admissibility-Preserving Control (APC) architecture in which an Admissibility-Preserving Input Realization (APIR) governs physical inputs and a logarithmic barrier coordinate represents the safety corridor. The synthesis yields an exact cascade in which exponentially decaying realization errors drive nonsymmetric consensus dynamics. For every compatible compact initial set, the closed-loop system admits a unique complete solution, renders the moving corridor and actuator intervals forward invariant with uniform margins, keeps commands bounded, and achieves exponential consensus. We derive direction-specific sufficient conditions under which positive and negative control demands remain within their corresponding actuator limits. The analysis yields a closed-form barrier-coordinate limit determined by the left Perron vector and initial APIR mismatch. Under strong connectivity and the stated gain and compatibility conditions, partial pinning propagates a constant barrier reference from a nonempty informed subset and assigns the induced safety corridor trajectory. A non-weight-balanced example illustrates the directional certificate and predicted collective motion.
GALACxIS Lab, Department of Aerospace Engineering, University of Cincinnati, Cincinnati, OH 45221, USA · Intelligent Systems and Control (ISaC) Lab, Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
This paper presents a low-complexity, model-free, output-feedback controller for a class of unknown time-varying nonlinear systems with unknown input constraints. The controller achieves the preset control accuracy when the actuator is not saturated and maintains flexible control accuracy after actuator saturation. This result extends existing constraint control methods for linear manifolds to a more general form, including the construction of nonlinear manifolds and various types of constraints, thereby achieving preset control accuracy within finite or fixed time. Additionally, flexible control under unknown saturation is achieved through the construction of an error-driven flexible constraint. Finally, second-order and higher-order control examples and simulations are provided.
Dianrui Mu, Changchun Hua, Yafeng Li +2
Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, China