Model Predictive Control with Preview

• Model Predictive Control with Preview is a control technique that uses anticipated exogenous signals, such as disturbances and references, to enhance decision-making over a finite prediction horizon.
• It integrates preview types like disturbance, reference, and cost previews into the optimization framework to adjust control actions proactively, ensuring constraint satisfaction and improved performance.
• Practical applications in automotive, railway, and robotics emphasize its ability to reduce energy consumption and improve tracking, despite increased computational demands in real-time scenarios.

Model Predictive Control (MPC) with preview refers to optimal control schemes that utilize explicit knowledge of future exogenous signals—such as disturbances, references, costs, or constraints—available in advance to the controller over a finite prediction horizon. This paradigm enables the predictive controller to proactively shape control actions in anticipation of upcoming operating conditions, leveraging vehicle connectivity, high-fidelity environmental sensing, or scenario-based prediction for improved performance in dynamic, constraint-laden systems.

1. Conceptual Foundation and Mathematical Formulation

The essential MPC-with-preview paradigm augments the canonical MPC optimal control problem by directly incorporating time-varying, previewed signals as parameters in the prediction model, cost function, and constraint definitions. Consider the general discrete-time nonlinear system

$x_{k+1} = f(x_k, u_k, w_k)$

where $x_k \in \mathbb{R}^n$ is the state, $u_k \in \mathbb{R}^m$ the control input, and $w_k \in \mathbb{R}^p$ a bounded exogenous signal. At each time $k$, a preview of the next $N$ realizations, $\{w(k|k), w(k+1|k), ..., w(k+N-1|k)\}$, is assumed available.

The corresponding finite-horizon OCP becomes: $$\begin{aligned} \min_{u_k,...,u_{k+N-1}} \quad & \sum_{i=0}^{N-1} l(x_{k+i|k},u_{k+i|k},w_{k+i|k}) + V_f(x_{k+N|k}) \ \textrm{s.t.} \qquad & x_{k+0|k} = x_k\ & x_{k+i+1|k} = f(x_{k+i|k},u_{k+i|k},w_{k+i|k})\ & x_{k+i|k} \in \mathcal{X}, \quad u_{k+i|k} \in \mathcal{U}\ & x_{k+N|k} \in \mathcal{X}_f \end{aligned}$$ This structure admits stage and terminal costs $l$, $V_f$, constraints, and even dynamics themselves parameterized by the previewed exogenous signals. Real implementations, as in automotive, railway, and robotics domains, tailor this structure to application-specific preview information: vehicle speed, road grade, traffic states, friction coefficients, or multi-scenario demand traces (Wang et al., 2018, Fang et al., 2022, Ozkan et al., 2021, Ewering et al., 2023, East et al., 2021).

2. Preview Types and Integration Strategies

2.1 Disturbance and Parameter Preview

Previewed exogenous disturbances or parameters—e.g., road grade, wind, friction, wave loads—are injected at each stage of the horizon as known values. This allows the prediction model to directly propagate their impact on future states and constraints, enabling the controller to actively exploit favorable previews or mitigate adverse effects. The augmentation of the system state with the disturbance-preview vector provides a rigorous basis for recursive feasibility and Input-to-State Stability (ISS) analysis under bounded, pre-bounded, or slowly-varying disturbances (Fang et al., 2022, Baldivieso-Monasterios et al., 2018).

2.2 Reference, Constraint, and Cost Preview

Preview can manifest as knowledge of future references, setpoints, or constraint bounds (e.g., target temperature bounds, lateral track coordinates, time-varying safety limits). This enables time-varying “soft” or “hard” comfort or safety envelopes to be imposed, e.g., adjusting cabin temperature upper bounds in anticipation of varying vehicle speed and thermal system efficiency (Wang et al., 2018). Similarly, future cost functions—arising in online learning MPC—are previewed in the horizon, enabling regret-driven adaptation in, e.g., data-driven energy management (Muthirayan et al., 2021, East et al., 2021).

2.3 Scenario-Based or Multi-Trajectory Preview

When direct forecasting is uncertain or unreliable, preview information is constructed as a finite set of plausible future scenarios, each encoding a full possible realization of exogenous signals (e.g., driver demand profiles, traffic evolutions). Scenario-MPC solves the OCP simultaneously for this ensemble, enforcing a common first-step control action and optimizing expected or worst-case performance (East et al., 2021). The final applied input thus reflects a weighted combination of likely future trajectories.

3. Recursive Feasibility and Stability With Preview

Integrating preview poses nontrivial challenges for recursive feasibility and closed-loop stability. Standard terminal ingredients—cost, policy, invariant sets—must be modified to account for the endpoint of the previewed signals. In the linear additive-disturbance setting, this is accomplished by translating the nominal terminal set and terminal cost to the steady-state offset induced by the terminal preview value (Baldivieso-Monasterios et al., 2018). For nonlinear systems, ISS-Lyapunov-based arguments and construction of terminal regions and costs augmented by preview yield recursive feasibility and robust stability under persistent or slowly-varying previews (Fang et al., 2022): $$V_f(f(x, u_f(x), w)) \le V_f(x) - l(x, u_f(x), w) - \sigma_1(\|x\|) + \delta_3(\|w\|)$$ where $\sigma_1$ and $\delta_3$ are class $\mathcal{K}_{\infty}$ and $\mathcal{K}$ functions quantifying robustness margins.

A central finding is that, assuming the previewed signals change only gradually (step-to-step Lipschitz continuity or maximum change $\lambda$), carefully designed terminal sets and value function sub-levels yield positively invariant tubes in the augmented (state, preview) space, thereby ensuring feasibility and a time-varying region of attraction (Baldivieso-Monasterios et al., 2018).

4. Computational and Implementation Considerations

Preview-based MPC can introduce significant additional real-time computational complexity. The need to process and embed preview signals at each horizon step (particularly when high-dimensional, scenario-based, or involving integer variables as in Mixed-Integer MPC) can obstruct real-time feasibility.

To address this, application-specific reductions are employed:

• For combinatorial preview (e.g., eco-coasting with discrete on/off), heuristic pre-scheduling based on offline DP allows relaxation of integer variables and acceleration of online NMPC to real-time (Yan et al., 2021).
• For LTI or analytically trainable preview structures, explicit state-space augmentation and fixed preview horizon permit pre-computation of gains or matrices, leading to update steps scaling as $\mathcal{O}(n^2)$ or better (Murooka et al., 29 May 2025, Caron et al., 2016).
• Scenario-MPC with long preview and large scenario ensembles is solvable via highly parallel ADMM, decoupling each scenario subproblem except for the coupling first-step constraint (East et al., 2021).

Hardware implementations in automotive, robotics, and railway demonstrate preview-based MPC solving complex nonlinear programs—with hundreds of variables and constraints—within tight deadlines (0.1–10 ms), leveraging tailored real-time SQP or direct multiple shooting in C/embedded toolchains (Tavolo et al., 4 Jun 2024, Ewering et al., 2023, Wang et al., 2018).

5. Domain-Specific Applications and Performance Gains

Table: Representative Applications and Preview Types

Domain	Preview Signal(s)	Quantitative Gain
Automotive A/C (Wang et al., 2018)	Vehicle speed (from V2X)	6–9% A/C energy
Truck Platooning (Ozkan et al., 2021)	Lead vehicle speed, traffic	17.5% platoon fuel
Railway (Ewering et al., 2023)	Track geometry, setpoint	30–40% RMS lateral
Connected EV Traction (Tavolo et al., 4 Jun 2024)	Friction ahead (V2X)	s_peak <0.05 from 0.85
Eco-coasting (Yan et al., 2021)	Road grade profile	6–12% fuel vs PI
Underwater (Walker et al., 2023)	Wave disturbance preview	51% reduction in pos. RMSE

Preview-aware MPC is particularly effective in energy and comfort management for electric and hybrid vehicles, longitudinal and lateral train motion control, and dynamic multi-contact humanoid gait generation, due to their structurally predictable exogenous signals. Competent exploitation of preview enables:

• selective shifting of “hard” control effort to windows of system efficiency (e.g., cooling during highway cruise, aggressive slip control when friction ahead is low),
• anticipation of “unfavorable” regimes by temporarily relaxing soft constraints or augmenting physical constraint bounds,
• enhanced disturbance rejection and tracking, with reduced constraint violation frequencies and improved comfort/safety indices.

6. Limitations, Robustness, and Research Directions

Preview-based MPC performance is tied directly to the accuracy, granularity, and availability of the preview itself. Key limitations include:

• Sensitivity to erroneous, delayed, or adversarially perturbed previews (V2X signal dropouts, fast-varying environments);
• Lack of full disturbance-model integration in core plant dynamics (as in (Wang et al., 2018), where speed preview alters only constraints, not the process model);
• Absence of richer comfort and robustness criteria, such as rate/derivative bounds or multi-dimensional uncertainty sets.

Current and future research aims involve:

• Integration of learned or scenario-based preview models to handle uncertainty and adversarial conditions, with provable bounds on constraint violation and regret (Muthirayan et al., 2021, East et al., 2021);
• Embedding multi-modal previews, e.g., weather or sun-load for thermal systems, with principled updating strategies as preview fidelity evolves in real time;
• Robustification techniques for managing abrupt preview discontinuities (using ISS tube-MPC, constraint tightening, min-max optimization);
• Hardware-in-the-loop experimental validation and scaled networked implementations (especially in V2X-dense or fully automated transport settings).

7. Comparative Performance and Theoretical Guarantees

Preview-enabled MPC often achieves performance close to that of a controller with perfect future information, and far surpasses non-previewed baselines. For online learning and regret scenarios, fixed-length preview suffices to yield sublinear dynamic regret (e.g., $\mathcal{O}(T^{2/3})$ with constant preview window), bridging the gap between real-time applicability and theoretical optimality (Muthirayan et al., 2021).

Formally, the integration of preview transforms the robust region of attraction and/or the ISS-tube of the controller: the union over all feasible previews strictly exceeds the region under nominal (no preview) MPC (Baldivieso-Monasterios et al., 2018). In practical implementations—especially networked, distributed, or scenario-based architectures—recursive feasibility and robust optimality are retained provided carefully designed terminal structures and sub-level sets in the augmented state-preview space.

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