Improved Sequential Model Predictive Control

• ISMPC is a control strategy that partitions complex optimal control problems into sequentially solvable convex subproblems for enhanced real-time applicability.
• It leverages space-encoding, subsystem decomposition, and switched constraint techniques to efficiently manage collision avoidance and stability.
• Algorithmic improvements result in increased corridor utilization and reduced constraint overhead, with proven benefits in AMR navigation and power electronics.

Improved Sequential Model Predictive Control (ISMPC) refers to a class of optimization-based control algorithms that reformulate standard Model Predictive Control (MPC) schemes as sequential or partitioned optimal control problems, enhancing computational tractability and real-time applicability especially in high-dimensional, constrained, or hybrid domains. Modern ISMPC frameworks leverage innovative space-encoding, subsystem decomposition, and constraint management techniques to yield high-performance, real-time controllers for applications such as autonomous mobile robots (AMRs) navigating in cluttered environments, power electronics, and large-scale linear systems (Qu et al., 15 Dec 2025, Grimm et al., 2020, Ling et al., 2011).

1. Core Principles and Problem Formulation

ISMPC derives from the need to address intractable or numerically expensive optimal control problems by systematically reformulating them as sequential or switched subproblems. The canonical ISMPC formulation for AMR navigation, for example, considers discrete-time nonholonomic robot kinematics: $\eta_{k+1} = \eta_k + \Delta T\,G(\eta_k)\,\nu_k$ with state $\eta = [x\, y\, \psi]^T$ and control input $\nu = [u\, v\, r]^T$, subject to hard constraints on velocities, workspace boundaries, and collision avoidance.

At each control step, a finite-horizon Optimal Control Problem (OCP) is solved: $$\min_{\nu_{0:N-1}}\quad J_N(\eta_{N}) + \sum_{k=0}^{N-1} J_k(\eta_k, \nu_k)$$ subject to system dynamics, actuator constraints, and sequentially switched convex corridor and barrier constraints (Qu et al., 15 Dec 2025).

In broader contexts, ISMPC encapsulates approaches such as Multiplexed Model Predictive Control (MMPC), where control channels or subsystems are updated sequentially rather than jointly, and two-stage decompositions seen in power electronics applications, where linear and nonlinear control objectives are decoupled for efficient search (Grimm et al., 2020, Ling et al., 2011).

2. Sequential Decomposition and Switched Constraint Schemes

A defining characteristic of ISMPC methods is the partitioning of complex, often mixed-integer or non-convex OCPs into sequentially or cyclically switched convex subproblems. For nonholonomic robot navigation, ISMPC combines:

• Multi-Directional Safety Rectangular Corridor (MDSRC) algorithm: Encodes the collision-free static workspace as a sequence of locally optimal, axis-aligned rectangular convex regions. At each waypoint, rectangular corridors are inflated in multiple candidate orientations, and the one offering maximal free area is selected. Static constraints thus become a small set of linear inequalities in local coordinates, significantly reducing constraint management overhead.
• Dynamic Control Barrier Function (D-CBF) inequalities: Dynamic obstacles are modeled as disks, and collision avoidance is enforced through linearized barrier function constraints, ensuring forward invariance of the safe set at each prediction step.

Sequential subsystem control, as in MMPC, assigns a cyclic update sequence $\sigma(k)$ across $m$ control channels, such that only one channel is updated per substep, distributing computation over a complete update cycle and enabling high disturbance rejection rates (Ling et al., 2011).

In power electronics applications, multi-stage ISMPC splits the OCP into a first-stage sphere-decoding (for linear costs) and a second-stage exhaustive search (for nonlinear coupling such as DC-link voltage balance), offering a tractable means to address otherwise prohibitive scale and nonlinearity (Grimm et al., 2020).

3. Algorithmic and Implementation Details

Efficient realization of ISMPC hinges on key design choices in constraint encoding, search organization, and solver selection. For AMR navigation in (Qu et al., 15 Dec 2025):

• Corridor parameters: $N_c=10$ candidate directions, $\Delta_L=0.1\,\mathrm{m}$ inflation step, maximum extension $L_{\max}=8\,\mathrm{m}$, $\Delta_s=0.3\,\mathrm{m}$ margin.
• Control limits: $|u|\leq 1.0\,\mathrm{m/s}$, $|r|\leq 1.5\,\mathrm{rad/s}$.
• Optimization: At each iteration, static corridors are updated periodically ($\sim$0.3 s or distance-triggered), and an NLP is solved (IPOPT/CasADi in C++), enforcing local corridor constraints, barrier inequalities, and dual-target cost structure.

For sphere-decoding-based sequential MPC (Grimm et al., 2020), the first subproblem is cast as an integer least-squares search, efficiently pruned via branch-and-bound. Only the $N_k$-best sequences are retained for each channel and combined in a small-scale exhaustive search. MMPC algorithms (Ling et al., 2011) sequence short QPs of size $O(N_u)$ for each input subproblem, and terminal cost structures ensure Lyapunov-decreasing closed-loop performance.

Table: Key Algorithmic Parameters in ISMPC Navigation (Qu et al., 15 Dec 2025)

Parameter	Value/Spec	Purpose
Sampling time ($\Delta T$)	$0.1\,s$	Discretization
Horizon ($N$)	$10$	Prediction depth
Number of directions ($N_c$)	$10$	Candidate corridor orientations
Extension step ($\Delta_L$)	$0.1\,m$	Corridor inflation granularity
Max. extension ($L_{\max}$)	$8\,m$	Largest allowed corridor size

4. Quantitative Performance and Real-time Characteristics

ISMPC architectures achieve significant improvements in both free-space utilization and computational feasibility. In AMR navigation benchmarks:

• Average corridor generation latency is $~3$ ms per waypoint (including all inflations).
• The mean corridor area increases by $41.1\%$ relative to single-orientation SRC/FSRC methods, with the number of active corridor constraints reduced by $35.9\%$.
• End-to-end MPC solve and actuation remains real-time feasible ($<5$ ms latency), enabling high-frequency navigation in highly cluttered environments.
• In multi-robot dynamic settings, ISMPC guarantees zero collisions (enforced by D-CBF) and produces smooth velocity profiles for agents exchanging goals.

Sphere-decoding ISMPC in power electronics delivers DC-link balance root-mean-square error (RMSE) up to $50\%$ lower than linearization-based or joint-MPC competitors at moderate additional computation, and supports adaptive trade-offs via key parameters $(N_h, N_k)$. MMPC achieves lower total computation in large-horizon problems while maintaining tight constraint satisfaction and disturbance rejection (Grimm et al., 2020, Ling et al., 2011).

5. Theoretical Guarantees and Performance Trade-offs

ISMPC frameworks explicitly address suboptimality versus computational speed. Switched or sequential constraint handling is theoretically justified through:

• Lyapunov or cost-to-go contraction: At each MPC step, strict decrease in a Lyapunov-like cost function is ensured (dual-target cost plus switching corridors).
• Barrier invariance: For dynamic constraints (e.g., D-CBF), forward invariance of the safe set is rigorously enforced.
• Periodic stability analysis: In cyclic update schemes, stability is established via periodic Riccati equations and terminal cost selection matching the underlying periodic control system (Ling et al., 2011).
• Suboptimality analysis: In MMPC and two-stage SMPC, the lost degrees of freedom per update are offset by higher update rates or tractable nonlinear searches, and a priori cost-difference estimates guide horizon and partition selection.
• Feasibility and robustness: Constraint tightening and augmented state formulations ensure feasible constraint management even under asynchronous or sequential updates.

A plausible implication is that ISMPC frameworks, when equipped with carefully designed switching logic and constraint families, can deliver provably stable and robust control in domains where classical (fully joint) MPC would prove intractable.

6. Application Domains and Future Directions

Originally developed for AMR navigation and power electronic converter control, ISMPC methodologies extend to any system where scalability and hard real-time constraints dominate. MMPC has demonstrated utility in high-dimensional linear plants, disturbance rejection in aerospace systems, and modular architectures for weakly coupled subsystems (Qu et al., 15 Dec 2025, Grimm et al., 2020, Ling et al., 2011).

Opportunities for future research include:

• Formal feasibility and stability proofs under time-varying and switching corridor constraint families in nonholonomic/heterogeneous systems (Qu et al., 15 Dec 2025).
• Integration of stochastic prediction modules for socially-aware navigation.
• Automatic selection of decomposition parameters (e.g., $N_k$, $N_h$) using data-driven or adaptive algorithms.
• Extension to fully distributed and asynchronous MPC architectures for large-scale networked robotic or process systems.

ISMPC thus provides a scalable, formally grounded, and empirically validated approach to constrained optimal control in computationally demanding settings, bridging the gap between classical MPC and modern autonomous systems.