---
title: Event-Driven Receding Horizon Control
url: https://www.emergentmind.com/topics/event-driven-receding-horizon-control
type: topic
---

# Event-Driven Receding Horizon Control

Event-driven receding horizon control (ED-RHC) is a hybrid optimal control paradigm characterized by intermittent, state-driven control updates rather than periodic time-based scheduling. Updates occur at discrete events defined by the system's evolution or the occurrence of exogenous and controllable triggers, with finite-horizon optimization solved at each event for near-future control actions. This methodology has been rigorously developed in linear-quadratic systems with limited actuation, multi-agent coordination, networked estimation, persistent monitoring, ride-sharing, and energy-aware robotic settings. The distinctive features include non-uniform control execution, combinatorial nonconvex optimization, and substantial computational and communication savings while maintaining provable stability and performance bounds.

## 1. Mathematical Formulation and Problem Classes

ED-RHC applies to a variety of system models, including discrete-time linear systems, multi-agent networked systems, and hybrid automata. In the canonical linear-quadratic setting, the system evolves as:

\[
x_{k+1} = A x_k + B u_k,\quad x_0 \text{ given},\quad x_k \in \mathbb{R}^n,\, u_k \in \mathbb{R}^m
\]

The cost over finite horizon $N$ is:

\[
J_N(x_0, \{u_k\}) = x_N^T P x_N + \sum_{k=0}^{N-1} (x_k^T Q x_k + u_k^T R u_k)
\]

Event-driven control restricts $u_k$ to zero at time-instants where $x_k$ is inside a dead-zone (e.g., $C_0 = \{x : \|x\|_\infty < \epsilon \}$). The optimization is:

\[
\min_{\{u_k\}} J_N(x_0, \{u_k\}) \quad \text{s.t. } u_k = 0 \,\forall\, k \in T,\, x_{k+1} = A x_k + B u_k
\]

where $T = \{ k : \|x_k\|_\infty < \epsilon \}$ is state-dependent and nonconvex [1701.04871].

In networked and multi-agent contexts (e.g., persistent monitoring, distributed estimation), each agent or controller solves distributed subproblems determining dwell times, target assignments, or action horizons based on local events such as arrivals, departures, uncertainty crossings, or neighbor coverage changes [2003.11713][2102.12963].

## 2. Event Definitions and Triggering Rules

Events are precisely defined state transitions or system changes that necessitate re-optimization. These include:

- **State threshold crossings**: When $x_k$ exits/enters the dead-zone $C_0$.
- **Agent arrivals/departures**: In network routing or multi-agent monitoring, events include agents reaching nodes or departing.
- **External requests or appearances**: New tasks, targets, or disturbances (e.g., passenger requests in ride-sharing [1901.01919], detection of new targets [1403.3434]).
- **Uncertainty or state milestones**: Target uncertainty hitting zero, or estimation error thresholds in distributed estimation [2009.11958].

Control is executed open-loop between events; re-optimization is only performed at the occurrence of events, substantially reducing computation relative to periodic MPC.

## 3. Finite-Horizon Optimal Control under Event Constraints

At each event, a finite-horizon open-loop optimal control problem is solved, subject to combinatorial event-driven constraints (e.g., state-dependent $u_k$ settings, feasible agent-task assignments). The optimization domains are typically nonconvex, due to implicit dependencies of the feasible set on future states and inputs.

Solution strategies include:

- **Exact enumeration**: Disjunctive quadratic programming over all possible event sequences, yielding the global optimum at exponential complexity [1701.04871].
- **Greedy and heuristic methods**: Greedy region assignment, active-target reduction, or finite heading sets in multi-agent and cooperative missions, enabling polynomial-time computation and near-optimality [1403.3434].
- **ADMM-based heuristics**: Consensus ADMM formulations, projecting iterates onto the nonconvex event-trigger constraints, with a final QP polish step [1701.04871].
- **Rollout and combinatorial search**: Rollout optimization over binary actuation sequences to promote sparsity in actuation and control performance, achieving performance guarantees above periodic baselines [2509.24799].

## 4. Receding Horizon Implementation and Distributed Schemes

ED-RHC operates in a receding horizon loop, triggered only at events:

- **Measurement**: At each event, measure current state or agent locations.
- **Finite-horizon solve**: Solve the event-constrained OCP for the horizon $N$ or a locally optimal planning window.
- **Apply control**: Execute only the first control action (or dwell-time/heading), then await next event.
- **Repeat**: Advance to next event and re-solve.

Distributed implementations are prevalent in networked systems, where each agent requires only local data (states of neighboring nodes), admits explicit closed-form or enumerative solutions, and exploits automatic (variable) horizon selection for parameter-free computation [2003.11713][2102.12963][2009.11958].

## 5. Theoretical Properties: Stability, Optimality, Performance Guarantees

ED-RHC schemes provide rigorous guarantees:

- **Practical stability** is established under stabilizability and suitable terminal cost/control law conditions. For discrete-time LQ systems, closed-loop trajectories converge to a $\infty$-norm ball $D_\mu$ whose radius depends on event threshold parameters and system matrices [1701.04871].
- **Optimality per event**: The event-driven structure allows for global optimality of the local subproblems at each event; the overall process approaches monotonic improvement due to automatic planning horizon optimization [2003.11713].
- **Unimodality**: The local RHCPs possess unimodal cost profiles under mild assumptions, enabling efficient scalar or bivariate minimization per agent [2009.11958].
- **Performance bounds**: Rollout-based event-driven controllers are provably within $O(1/T)$ per-step cost of the optimal periodic controller, while Lyapunov drift conditions ensure mean-square stability [2509.24799].
- **Non-Zeno behavior**: Event-driven updates are guaranteed to occur at nonzero intervals, preventing pathological re-optimization [2003.11713].

## 6. Application Areas and Practical Effectiveness

ED-RHC has been successfully applied across diverse domains:

- **Networked linear systems**: Threshold-based event-triggered MPC reduces control transmissions and computation, yielding substantial communication savings with limited performance degradation [1701.04871].
- **Ride-sharing and transport systems**: Discrete event-driven RHC drastically reduces optimization frequency and search size compared to time-driven MPC, achieving nearly $2\times$ improvement in weighted-sum metrics over greedy assignment heuristics and real-time implementation on city-scale networks [1901.01919].
- **Multi-agent cooperative reward collection**: Event-driven CRH controllers outperform original infinite-dimensional MPC and greedy cycle planners, with $20$–$130\%$ reward increase in uncertain environments, stabilized trajectories, and finite heading set reduction [1403.3434].
- **Persistent monitoring and estimation**: Event-driven RHC excels in network surveillance tasks with energy-aware or first-order agent dynamics, parametrically trading off uncertainty reduction and energy usage; closed-form optimization, distributed computation, and robustness to disturbances and partial information are demonstrated [2102.12963][2003.11713].
- **Disturbance-aware predictive control**: Event-driven model predictive controllers for hybrid automaton-modeled power inverters exploit disturbance estimation via recursive least squares, outperform traditional PWM controllers in tracking error, settling time, and robustness to load-shifts [2012.11824].
- **Sparsity-promoting control**: Rollout-based event-driven schemes balance actuation frequency and control performance, with explicit stability and near-optimal cost guarantees [2509.24799].

## 7. Design Considerations, Parameter Selection, and Extensions

Key guidelines for ED-RHC design:

- **Threshold selection**: Choosing the event-trigger threshold trades off between communication savings and performance; moderate threshold values typically provide substantial savings with modest impact [1701.04871].
- **Horizon choice**: Larger finite horizons improve performance and stability but increase computational burden; event-driven approaches with automatic horizon optimization avoid manual tuning [2003.11713].
- **Solution strategy**: Exact enumeration is viable for low-dimensional state spaces; otherwise, greedy, ADMM, rollout, or combinatorial heuristics provide scalable approximations with explicit performance bounds.
- **Robustness and feasibility**: Distributed event-driven controllers inherently adapt to disturbances by triggering earlier/later updates, and always admit a feasible "stay-put" option [2102.12963][2003.11713].
- **Learning-based acceleration**: Machine learning classifiers can be integrated to predict optimal actions per event, reducing computational load by bypassing exhaustive search, with negligible loss in average performance [2009.11958].
- **Potential extensions**: Ongoing developments include incorporating online terminal cost estimation, handling nontrivial agent dynamics (acceleration), adapting to time-varying networks, and integrating high-level task allocation [2003.11713].

A plausible implication, given the breadth of applications and robust theoretical underpinnings, is that ED-RHC forms a foundational architecture for scalable, efficient, and provably-stable optimal control in cyber-physical, networked, and multi-agent systems subject to resource-constrained or intermittent actuation scenarios.

Source: https://www.emergentmind.com/topics/event-driven-receding-horizon-control