State-Dependent Riccati Equation Techniques in Nonlinear Control Systems

The state-dependent Riccati equation (SDRE) framework offers a systematic route to optimal control for a broad class of nonlinear systems. By expressing the nonlinear dynamics in a state-dependent coefficient form, the SDRE method casts the control problem into a sequence of algebraic Riccati equations parameterised by the current state. This pseudo-linearisation preserves key nonlinear features while enabling feedback gains to be computed in real time. Variants such as the output‐ and state-dependent Riccati equation (OSDRE) extend this approach to systems with partial state measurements, and the state-dependent differential Riccati equation (SDDRE) further generalises to time-varying or infinite-horizon settings. Together, these techniques bridge the gap between classical linear quadratic regulators and modern nonlinear control, delivering stabilising and near-optimal performance across applications that range from high-precision motor drives to aerial robotics and space manipulators. The global significance of the approach lies in its blend of theoretical rigour—guaranteeing local stability and convergence properties—with practical implementability on real-time embedded platforms. Concrete demonstrations include sensorless control of permanent-magnet synchronous motors, collision-tolerant guidance of free-floating manipulators in orbit, and aerobatic flight regulation of quadrotor drones, illustrating how SDRE-based controllers meet demanding performance, robustness and computational constraints simultaneously.

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State-Dependent Riccati Equation Techniques in Nonlinear Control Systems publication trend

The graph below shows the total number of articles in state-dependent riccati equation techniques in nonlinear control systems across all publications each year (not limited to Nature Index journals).

Technical terms

State-dependent Riccati equation (SDRE): A method that transforms nonlinear control problems into algebraic Riccati equations with coefficients that depend on the system state, enabling local optimal feedback design.

Output- and state-dependent Riccati equation (OSDRE): An extension of SDRE that accommodates systems with partial state measurements by formulating the Riccati equation in terms of both outputs and states.

State-dependent differential Riccati equation (SDDRE): A time-varying generalisation of SDRE for infinite-horizon or continuous-time regulation problems in which the Riccati equation evolves differentially with the state.

Pseudo-linearisation: A technique that represents nonlinear dynamics as a state-dependent linear system, preserving nonlinear characteristics while enabling linear control tools.

Affine nonlinear system: A dynamical system whose vector field can be written as the sum of a state-dependent linear term and an input-dependent term, facilitating SDRE formulation.

References

1. Observer-Based Suboptimal Controller Design for Permanent Magnet Synchronous Motors: State-Dependent Riccati Equation Controller and Impulsive Observer Approaches. Computers (2024).
2. Free-floating space manipulator impacting a floating object: Modeling and output SDRE controller design. Aerospace Science and Technology (2024).
3. Quaternion-based state-dependent differential Riccati equation for quadrotor drones: Regulation control problem in aerobatic flight. Robotica (2022).